GroupTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : GroupTheory/GeneralLinearGroup

GroupTheory

  

GeneralLinearGroup

  

construct a permutation group isomorphic to the General Linear Group over a finite field

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GeneralLinearGroup(n, q)

GL( n, q )

Parameters

n

-

a positive integer

q

-

power of a prime number

Description

• 

The general linear group GLn,q is the set of all nonsingular n×n matrices over a finite field of size q, where q is a prime power.

• 

If n and q are positive integers, then the GeneralLinearGroup( n, q ) command returns a permutation group isomorphic to the general linear group  GLn,q for the implemented ranges of the parameters n and q. Otherwise, a symbolic group is returned, for which Maple can do some limited computations.

• 

The implemented ranges for n and q are as follows:

n=2

q100

n=3

q20

n=4

q10

n=5

q5

n=6,7,8,9,10

q=2

• 

The abbreviation GL( n, q ) is available as a synonym for GeneralLinearGroup( n, q ).

• 

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

Examples

withGroupTheory:

GeneralLinearGroup2,3

GL2,3

(1)

GGL2,5

GGL2,5

(2)

GroupOrderG

480

(3)

csCompositionSeriesG

csGL2,55,156,167,178,189,1910,2011,2112,2213,2314,24,1,17,3,92,23,4,115,20,15,106,12,18,247,8,19,1613,14,21,22,1,22,3,142,8,4,165,20,15,106,7,18,199,11,17,2312,13,24,21,1,23,3,112,9,4,175,6,15,187,13,19,218,22,16,1410,12,20,241,32,45,156,187,198,169,1710,2011,2312,2413,2114,22

(4)

seqGroupOrderS,S=cs

480,240,120,2,1

(5)

GroupOrderGL4,3

24261120

(6)

ClassNumberGL31,q

q31q15q14q13q12q11q10+2q8+3q7+4q6+q53q43q3+q

(7)

GroupOrderGLn,q

k=0n1qnqk

(8)

GroupOrderGL3,q

q31q3qq3q2

(9)

GroupOrderDerivedSubgroupGLn,q

qn2k=1n1qk+11

(10)

Compatibility

• 

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

• 

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

• 

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

See Also

GroupTheory[GeneralOrthogonalGroup]

GroupTheory[GeneralUnitaryGroup]

GroupTheory[GroupOrder]

GroupTheory[ProjectiveGeneralLinearGroup]