construct a permutation group isomorphic to a projective special unitary group - Maple Help

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GroupTheory[ProjectiveSpecialUnitaryGroup] - construct a permutation group isomorphic to a projective special unitary group

Calling Sequence

ProjectiveSpecialUnitaryGroup( n, q )

PSU( n, q )

Parameters

n

-

a positive integer

q

-

power of a prime number

Description

• 

The projective special unitary group PSUn,q, over the field with q2 elements, is the quotient of the special unitary group SUn,q by its center.

• 

Note that for n=2 the groups PSUn,q and PSLn,q are isomorphic.

• 

The ProjectiveSpecialUnitaryGroup( n, q ) command returns a permutation group isomorphic to the projective special unitary group PSUn,q for values of the parameters n and q in the implemented ranges.

• 

The implemented ranges for n and q are as follows:

n=2

q241

n=3

q16

n=4

q5

n=5

q4

n=6

q3

n=7,8

q=2

• 

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

• 

The command PSU( n, q ) is provided as an abbreviation.

Examples

withGroupTheory:

G:=ProjectiveSpecialUnitaryGroup3,3

G:=PSU3,3

(1)

DegreeG

28

(2)

GeneratorsG

2,173,274,75,246,138,119,2210,2112,1416,2018,1925,26,1,3,8,17,18,52,25,9,28,23,74,10,2211,12,26,24,27,1513,19,16,21,20,14

(3)

GroupOrderPSU5,3

258190571520

(4)

GroupOrderPSU4,q

q6q21q3+1q41igcd4,q+1

(5)

See Also

GroupTheory[Degree], GroupTheory[Generators], GroupTheory[GroupOrder], GroupTheory[ProjectiveSpecialLinearGroup], GroupTheory[SpecialUnitaryGroup]


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