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GroupTheory

  

SpecialLinearGroup

  

construct a permutation group isomorphic to a special linear group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

SpecialLinearGroup(n, q)

SL(n, q)

Parameters

n

-

a positive integer

q

-

power of a prime number

Description

• 

The special linear group SLn,q  is the set of all n×n nonsingular matrices over a finite field of size q whose determinant is 1.

• 

The SpecialLinearGroup( n, q ) command returns a permutation group isomorphic to the special linear group SLn,q  for values of n and q in the implemented ranges.

• 

The implemented ranges for the parameters 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

• 

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

• 

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

Examples

withGroupTheory:

SpecialLinearGroup3,2

SL3,2

(1)

GSL2,3

GSL2,3

(2)

GroupOrderG

24

(3)

GroupOrderSL4,q

q6q21q31q41

(4)

GSL2,5

GSL2,5

(5)

IsPerfectG

true

(6)

Compatibility

• 

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

• 

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

• 

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

See Also

GroupTheory[GeneralLinearGroup]

GroupTheory[ProjectiveSpecialLinearGroup]

GroupTheory[SpecialUnitaryGroup]