GroupTheory/ReducedDegreePermGroup - Maple Help
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GroupTheory

  

ReducedDegreePermGroup

  

try to find an isomorphic permutation group of smaller degree

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ReducedDegreePermGroup( G )

Parameters

G

-

PermutationGroup; a permutation group

Description

• 

The ReducedDegreePermGroup( G ) command returns a permutation group isomorphic (as an abstract group) with possibly smaller degree, if one can be found.

Examples

withGroupTheory:

GSmallGroup48,15

G < a permutation group on 48 letters with 5 generators >

(1)

DegreeG

48

(2)

RReducedDegreePermGroupG

R2&comma;83&comma;46&comma;79&comma;1011&comma;2012&comma;1913&comma;1614&comma;1517&comma;1821&comma;2422&comma;23&comma;1&comma;23&comma;94&comma;85&comma;106&comma;117&comma;1213&comma;2114&comma;2215&comma;1916&comma;2017&comma;2318&comma;24&comma;1&comma;6&comma;72&comma;11&comma;123&comma;13&comma;144&comma;15&comma;165&comma;17&comma;188&comma;19&comma;209&comma;21&comma;2210&comma;23&comma;24

(3)

DegreeR

24

(4)

It is not always possible to produce an isomorphic permutation group with smaller degree.

GCyclicGroup9

GC9

(5)

DegreeG

9

(6)

RReducedDegreePermGroupG

RC9

(7)

DegreeR

9

(8)

On the other hand, particularly for groups produced either from a finitely presented group (which are often regular), or via a linear or projective action on a vector space, the degree can be reduced substantially.

GMathieuGroup11&comma;&apos;form&apos;&equals;fpgroup

Ga&comma;ba2&comma;b4&comma;ab2ab2ab2ab2ab2ab2&comma;ababab-1abab2ab-1abab-1ab-1&comma;ababababababababababab

(9)

PPermutationGroupG&colon;

DegreeP

7920

(10)

IsRegularP

true

(11)

RReducedDegreePermGroupP

R1&comma;24&comma;57&comma;910&comma;11&comma;1&comma;2&comma;4&comma;35&comma;6&comma;8&comma;79&comma;1011&comma;12

(12)

DegreeR

12

(13)

See Also

GroupTheory

GroupTheory[Degree]