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GroupTheory

  

GeneralOrthogonalGroup

  

construct a permutation group isomorphic to a general orthogonal group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

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

with(GroupTheory):

G := GeneralOrthogonalGroup( 0, 7, 2 );

G:=GO7,2

(1)

Generators( G );

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 := GeneralOrthogonalGroup( 1, 4, 5 );

G:=GO4,5

(3)

GroupOrder( G );

28800

(4)

G := GeneralOrthogonalGroup( -1, 4, 5 );

G:=GO4,5

(5)

Degree( G );

104

(6)

GroupOrder( G );

31200

(7)

GroupOrder( GeneralOrthogonalGroup( 0, 7, 3 ) );

18341406720

(8)

GroupOrder( GeneralOrthogonalGroup( 1, 8, 2 ) );

348364800

(9)

GroupOrder( GeneralOrthogonalGroup( -1, 8, 2 ) );

394813440

(10)

Compatibility

• 

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

• 

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

See Also

GroupTheory[Degree]

GroupTheory[GeneralLinearGroup]

GroupTheory[GroupOrder]

GroupTheory[SpecialOrthogonalGroup]