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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.

• 

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.

• 

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 ).

Examples

withGroupTheory:

GeneralLinearGroup2,3

GL2,3

(1)

GL4,3

GL4,3

(2)

GroupOrderGL3,q

q31q3qq3q2

(3)

Compatibility

• 

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

• 

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

See Also

GroupTheory[GeneralOrthogonalGroup]

GroupTheory[GeneralUnitaryGroup]

GroupTheory[GroupOrder]

GroupTheory[ProjectiveGeneralLinearGroup]

 


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