construct a permutation group isomorphic to a general orthogonal group - Maple Help

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GroupTheory[GeneralOrthogonalGroup] - construct a permutation group isomorphic to a general orthogonal group

Calling Sequence

GeneralOrthogonalGroup(d, n, q)

Parameters

d

-

0, 1 or -1

n

-

a positive integer

q

-

power of a prime number

Description

• 

The general orthogonal group GOd,n,q is the set of all n×n matrices over the field with q elements that respect a non-singular quadratic form. The value of d must be 0 for odd n, or 1 or 1 for even n.

• 

The GeneralOrthogonalGroup( d, n, q ) command returns a permutation group isomorphic to the general orthogonal group GOd,n,q for the implemented values of d, n and q.

• 

The implemented ranges for n and q are as follows:

n=2

q100

n=3

q20

n=4

q10

n=5

q5

n=6,7,8

q=3

n=9,10,11

q=2

Examples

withGroupTheory:

G:=GeneralOrthogonalGroup0,7,2

G:=GO7,2

(1)

GeneratorsG

5,67,98,1110,1412,1613,1815,2117,2319,2622,2924,3125,3327,3630,3934,4335,4538,4740,4942,5244,4850,5451,5855,6156,57,2,3,4,5,7,106,8,12,17,24,329,13,19,27,37,4711,15,14,20,28,3816,22,23,30,40,5018,25,34,44,54,2126,3531,41,51,43,49,5733,42,53,60,61,4536,46,5539,48,5652,59,62,63,64,58

(2)

G:=GeneralOrthogonalGroup1,4,5

G:=GO4,5

(3)

GroupOrderG

28800

(4)

G:=GeneralOrthogonalGroup1,4,5

G:=GO4,5

(5)

DegreeG

104

(6)

GroupOrderG

31200

(7)

GroupOrderGeneralOrthogonalGroup0,7,3

18341406720

(8)

GroupOrderGeneralOrthogonalGroup1,8,2

348364800

(9)

GroupOrderGeneralOrthogonalGroup1,8,2

394813440

(10)

See Also

GroupTheory[Degree], GroupTheory[GeneralLinearGroup], GroupTheory[GroupOrder], GroupTheory[SpecialOrthogonalGroup]


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