GroupTheory/ProjectiveGeneralSemilinearGroup - Maple Help
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GroupTheory

  

ProjectiveGeneralSemilinearGroup

  

construct a permutation group isomorphic to the General Semi-linear Group over a finite field

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ProjectiveGeneralSemilinearGroup( n, q )

PGammaL( n, q )

Parameters

n

-

a positive integer

q

-

a power of a prime number

Description

• 

The projective general semi-linear group PΓLn,q is the quotient of the group ΓLn,q of all semi-linear transformations of an n-dimensional vector space over the field with q elements, by the center of GLn,q . It is isomorphic to a semi-direct product of the general linear group GLn,q with the Galois group of the field with q elements over its prime sub-field. Thus, if q is prime, then PΓLn,q and GLn,q are equal.

• 

If n is a positive integer, and q is a prime power, then the ProjectiveGeneralSemilinearGroup( n, q ) command returns a permutation group isomorphic to the projective general semi-linear group PΓLn,q . Otherwise, a symbolic group is returned, with which Maple can do some limited computations.

• 

The abbreviation PGammaL( n, q ) is available as a synonym for ProjectiveGeneralSemilinearGroup( n, q ).

Examples

withGroupTheory:

GProjectiveGeneralSemilinearGroup2,4

G2,3,4,1,2,5,3,4

(1)

GroupOrderG

120

(2)

AreIsomorphicG,Symm5

true

(3)

GPGammaL2,5

G2,4,5,3,1,5,62,3,4

(4)

GroupOrderG

120

(5)

AreIsomorphicG,Symm5

true

(6)

GPGammaL2,9

G2,8,4,5,3,6,7,9,1,3,104,8,65,9,7,4,75,86,9

(7)

GroupOrderG

1440

(8)

ctCharacterTableG

Displayct

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    t-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></\
    Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksV\
    HlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' draw\
    label='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell c\
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    3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' draw\
    label='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></\
    Table-Cell></Table-Row><Table-Row align='top' separator='true'><Table-Cell columnspan='1' backgroundstyle='1' rowspan='1' fillcolor='[245,255,250]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbWlHNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EnY2hpX18zNiI='>LUkjbWlHNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EnY2hpX18zNiI=</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-eq\
    uation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentatio\
    n' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMT\
    Yi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjb\
    W5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hi\
    de-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMT\
    Yi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-eq\
    uation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentatio\
    n' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell></Table-Row><Table-Row align='top' separator='true'><Table-Cell columnspan='1' backgroundstyle='1' rowspan='1' fillcolor='[245,255,250]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbWlHNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EnY2hpX180NiI='>LUkjbWlHNiQlKnByb3RlY3RlZEcvJS\
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    /Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMzYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMzYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5H\
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    NiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-\
    output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field><\
    /Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5H\
    NiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell></Table-Row><Table-Row align='top' separator='true'><Table-Cell columnspan='1' backgroundstyle='1' rowspan='1' fillcolor='[245,255,250]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbWlHNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EnY2hpX184NiI='>LUkjbWlHNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EnY2hpX184NiI=</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]\
    ' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiOTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiOTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMzYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksV\
    HlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMzYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2\
    D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide\
    -input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX\
    3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2\
    D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group \
    view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksV\
    HlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell></Table-Row><Table-Row align='top' separator='true'><Table-Cell columnspan='1' backgroundstyle='1' rowspan='1' fillcolor='[245,255,250]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' l\
    ayout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbWlHNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EnY2hpX185NiI='>LUkjbWlHNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EnY2hpX185NiI=</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EjMTA2Ig=='>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EjMTA2Ig==</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan=\
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    i'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMjYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMjYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' l\
    ayout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMTYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MjYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7MjYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan=\
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    ble='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7NDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1ErJnVtaW51czA7NDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMjYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMjYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' vi\
    sible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZ\
    XNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D In\
    put' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-inp\
    ut='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equatio\

    n></Text-field></Input></Group></Table-Cell><Table-Cell columnspan='1' backgroundstyle='0' rowspan='1' fillcolor='[255,255,255]' visible='true'><Group view='presentation' hide-input='false' hide-output='false' inline-output='false' drawlabel='true'><Input><Text-field alignment='centred' style='Text' layout='Normal'><Equation executable='false' style='2D Input' input-equation='' display='LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi'>LUkjbW5HNiQlKnByb3RlY3RlZEcvJSttb2R1bGVuYW1lR0ksVHlwZXNldHRpbmdHNiRGJSUoX3N5c2xpYkc2I1EiMDYi</Equation></Text-field></Input></Group></Table-Cell></Table-Row></Table></Worksheet>", state = "", minimal = true

DrawNormalSubgroupLatticeG

GroupOrderPGammaL3&comma;8

49448448

(9)

GroupOrderPGammaLn&comma;q

logpqk=0n1qnqkq1

(10)

GroupOrderPGammaL5&comma;q

logpqq51q5qq5q2q5q3q5q4q1

(11)

See Also

GF

GroupTheory[GeneralLinearGroup]

GroupTheory[GroupOrder]

GroupTheory[logp]

GroupTheory[SpecialSemilinearGroup]