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GroupTheory

  

SpecialOrthogonalGroup

  

construct a permutation group isomorphic to a special orthogonal group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

SpecialOrthogonalGroup(d, n, q)

Parameters

d

-

0, 1 or -1

n

-

a positive integer

q

-

power of a prime number

Description

• 

The special orthogonal group SOn,q is the set of all n×n matrices over the field with q elements that respect a non-singular quadratic form and have determinant equal to 1. The value of d must be 0 for odd values of n, or 1 or 1 for even values of n. Note that for even values of q the groups SOn,q and GOn,q are isomorphic.

• 

The SpecialOrthogonalGroup( d, n, q ) command returns a permutation group isomorphic to the special orthogonal group SOn,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

q100

n=3

q20

n=4

q10

n=5

q5

n=6,7,8

q=3

Examples

withGroupTheory:

SpecialOrthogonalGroup0,9,2

GO9,2

(1)

GSpecialOrthogonalGroup1,4,7

GSO4,7

(2)

DegreeG

128

(3)

GroupOrderG

112896

(4)

IsTransitiveG

true

(5)

GSpecialOrthogonalGroup1,4,7

GSO4,7

(6)

DegreeG

100

(7)

GroupOrderG

117600

(8)

IsTransitiveG

true

(9)

GroupOrderSpecialOrthogonalGroup0,7,3

9170703360

(10)

Compatibility

• 

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

• 

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

See Also

GroupTheory[Degree]

GroupTheory[GeneralOrthogonalGroup]

GroupTheory[GroupOrder]

GroupTheory[IsTransitive]