GroupTheory/AffineGeneralLinearGroup - Maple Help
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GroupTheory

  

AffineGeneralLinearGroup

  

construct the affine general linear group as a permutation group

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

AffineGeneralLinearGroup( n, q )

AGL( n, q )

Parameters

n

-

a positive integer

q

-

a prime power greater than 1

Description

• 

The affine general linear group AGLn,q is the semi-direct product of the general linear group GLn,q with the natural module of dimension n over the field with q elements.

• 

The AffineGeneralLinearGroup command produces a permutation group isomorphic to the group AGLn,q.

Examples

withGroupTheory:

GAffineGeneralLinearGroup1,2

GAGL1,2

(1)

GAGL1,2

GAGL1,2

(2)

GAGL1,3

GAGL1,3

(3)

AreIsomorphicG,Symm3

true

(4)

GAGL1,4

GAGL1,4

(5)

AreIsomorphicG,Alt4

true

(6)

GAGL1,5

GAGL1,5

(7)

IsFrobeniusGroupG

true

(8)

PermGroupRankG

2

(9)

GAGL2,2

GAGL2,2

(10)

AreIsomorphicG,Symm4

true

(11)

GAGL2,3

GAGL2,3

(12)

TransitivityG

2

(13)

PermGroupRankG

2

(14)

SStabilizer1,G

S4,6,57,8,9,2,8,53,6,9,2,9,6,4,3,5,8,7

(15)

AreIsomorphicS,GL2,3

true

(16)

GAGL3,2

GAGL3,2

(17)

IsPrimitiveG

true

(18)

EARNSG

1,23,45,67,8,1,52,63,74,8,1,32,45,76,8

(19)

TransitivityG

3

(20)

AreIsomorphicStabilizer1,G,GL3,2

true

(21)

GAGL3,3

GAGL3,3

(22)

TransitivityG

2

(23)

PermGroupRankG

2

(24)

GroupOrderStabilizer1,G=GroupOrderGL3,3

11232=11232

(25)

EARNSG

1,19,102,20,113,21,124,22,135,23,146,24,157,25,168,26,179,27,18,1,4,72,5,83,6,910,13,1611,14,1712,15,1819,22,2520,23,2621,24,27,1,3,24,6,57,9,810,12,1113,15,1416,18,1719,21,2022,24,2325,27,26

(26)

See Also

GroupTheory[AffineSpecialLinearGroup]

GroupTheory[GeneralLinearGroup]