ProjectiveSpecialLinearGroup - Maple Help
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GroupTheory

  

ProjectiveSpecialLinearGroup

  

construct a permutation group isomorphic to a projective special linear group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

ProjectiveSpecialLinearGroup(n, q)

PSL(n, q)

Parameters

n

-

a positive integer

q

-

power of a prime number

Description

• 

The projective special linear group  is the quotient of the special linear group  by its center.

• 

The ProjectiveSpecialLinearGroup( n, q ) command returns a permutation group isomorphic to the projective special linear group  .

• 

If either, or both, of n and q is non-numeric, then a symbolic group representing the symplectic group is returned.

• 

The command PSL( n, q ) is provided as an abbreviation.

• 

In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.

Examples

(1)

(2)

Note that PSL( 3, 4 ) has the same order as the alternating group of degree 8.

(3)

(4)

However, PSL( 3, 4 ) and Alt( 8 ) are not isomorphic.  First, Alt( 8 ) has an element of order equal to 15.

(5)

(6)

Next, there is no element of order 15 in PSL( 3, 4 ).

(7)

This shows that there are two non-isomorphic simple groups of order 20160.

(8)

(9)

Several among the small projective special linear groups are isomorphic to alternating groups.

(10)

(11)

(12)

(13)

(14)

Compatibility

• 

The GroupTheory[ProjectiveSpecialLinearGroup] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

• 

The GroupTheory[ProjectiveSpecialLinearGroup] command was updated in Maple 2020.

See Also

GroupTheory[GroupOrder]

GroupTheory[IsSimple]

GroupTheory[ProjectiveSpecialUnitaryGroup]

GroupTheory[SpecialLinearGroup]

 


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