construct a permutation group isomorphic to a projective general linear group - Maple Help

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GroupTheory[ProjectiveGeneralLinearGroup] - construct a permutation group isomorphic to a projective general linear group

Calling Sequence

ProjectiveGeneralLinearGroup(n, q)

PGL(n, q)

Parameters

n

-

a positive integer

q

-

power of a prime number

Description

• 

The projective general linear group PGLn,q is the quotient of the general linear group GLn,q by its center.

• 

The ProjectiveGeneralLinearGroup( n, q ) command returns a permutation group isomorphic to the projective general linear group PGLn,q. The PGL(n, q) command is provided as an alias.

• 

The 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

Examples

withGroupTheory:

G:=ProjectiveGeneralLinearGroup2,49

G:=PGL2,49

(1)

GeneratorsG

3,50,49,48,47,46,45,44,8,43,42,41,40,39,38,37,7,36,35,34,33,32,31,30,6,29,28,27,26,25,24,23,5,22,21,20,19,18,17,16,4,15,14,13,12,11,10,9,1,2,63,4,89,25,3310,20,3711,32,2412,15,4113,38,1614,30,2317,31,1918,44,4721,46,4322,39,4926,34,5027,48,3528,42,4029,45,36

(2)

G:=ProjectiveGeneralLinearGroup5,2

G:=PGL5,2

(3)

GroupOrderG

9999360

(4)

GroupOrderPGL4,3

12130560

(5)

AreIsomorphicPGL2,3,Symm4

true

(6)

AreIsomorphicPGL2,5,Symm5

true

(7)

See Also

GroupTheory[GeneralLinearGroup], GroupTheory[GroupOrder]


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