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GroupTheory

  

SpecialUnitaryGroup

  

construct a permutation group isomorphic to a special unitary group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

SpecialUnitaryGroup(n, q)

Parameters

n

-

a positive integer

q

-

power of a prime number

Description

• 

The special unitary group SUn,q  is the set of all n x n matrices over the field with q2 elements whose determinant is 1 and respect a fixed nondegenerate sesquilinear form.

• 

The SpecialUnitaryGroup( n, q ) command returns a permutation group isomorphic to the special unitary group  SUn,q  .

• 

Note that for n=2 the groups SUn,q  and SLn,q  are isomorphic so the latter is returned in this case.

• 

The ranges for n and q are as follows:

n=2

q100

n=3

q10

n=4

q4

n=5

q3

n=6,7

q=2

• 

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

GSpecialUnitaryGroup3,2

GSU3,2

(1)

GeneratorsG

2,3,5,94,7,13,226,11,19,268,15,17,2010,18,25,2412,21,27,23,1,2,4,8,16,24,21,7,14,11,20,273,6,12,5,10,9,17,18,19,25,22,2613,23,15

(2)

IsTransitiveG

true

(3)

GroupOrderSpecialUnitaryGroup4,2

25920

(4)

GSpecialUnitaryGroup2,23

GSL2,23

(5)

ClassNumberG

27

(6)

GroupOrderSpecialUnitaryGroup3,q

q3q21q3+1

(7)

MinPermRepDegreeSpecialUnitaryGroup3,5

378

(8)

Compatibility

• 

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

• 

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

• 

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

See Also

GroupTheory

GroupTheory[ClassNumber]

GroupTheory[Generators]

GroupTheory[GroupOrder]

GroupTheory[IsTransitive]

GroupTheory[ProjectiveSpecialUnitaryGroup]

GroupTheory[SpecialLinearGroup]