GroupTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : GroupTheory package : GroupTheory/GeneralUnitaryGroup

GroupTheory

  

GeneralUnitaryGroup

  

construct a permutation group isomorphic to a general unitary group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GeneralUnitaryGroup(n, q)

Parameters

n

-

a positive integer

q

-

power of a prime number

Description

• 

The general unitary group GUn,q (often denoted by Un,q) is the group of all n×n matrices over the field with q2 elements, where q is a prime power, that respect a fixed nondegenerate sesquilinear form.

• 

The GeneralUnitaryGroup( n, q ) command returns a permutation group isomorphic to the general unitary group GUn,q for the implemented ranges of the parameters n and q.

• 

The implemented ranges for n and q are as follows:

n = 2

q <= 20

n = 3

q <= 5

n = 4

q <= 4

n = 5, 6

q = 2

• 

If either, or both, of n and q is non-numeric, then a symbolic group representing the general unitary group is returned.

Examples

withGroupTheory&colon;

GeneralUnitaryGroup2&comma;2

GU2&comma;2

(1)

GroupOrderGeneralUnitaryGroup2&comma;4

300

(2)

GroupOrderGeneralUnitaryGroup4&comma;q

q&plus;1q6q21q3&plus;1q41

(3)

simplifyGroupOrderGeneralUnitaryGroup2&comma;3k

81k&plus;27k9k3k

(4)

Compatibility

• 

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

• 

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

See Also

GroupTheory[GeneralLinearGroup]

GroupTheory[GroupOrder]

GroupTheory[ProjectiveGeneralUnitaryGroup]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam