SpecialOrthogonalGroup - Maple Help
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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)

SO(d, n, q)

Parameters

d

-

0, 1 or -1

n

-

a positive integer

q

-

power of a prime number

Description

• 

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

• 

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

• 

If either or both of the parameters n and q is non-numeric, then a symbolic group representing the indicated special orthogonal group is returned. (The argument d must be numeric, equal to one of ,  or .)

• 

The command SO(d, n, q) is provided as an alias.

• 

In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.

Examples

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

C

1a

2a

2b

2c

3a

3b

3c

3d

4a

4b

4c

4d

6a

6b

6c

6d

8a

8b

12a

12b

|C|

1

1

18

72

8

8

32

32

6

6

36

36

8

8

32

32

72

72

48

48

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Compatibility

• 

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

• 

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

• 

The GroupTheory[SpecialOrthogonalGroup] command was updated in Maple 2020.

See Also

GroupTheory[Degree]

GroupTheory[GeneralOrthogonalGroup]

GroupTheory[GroupOrder]

GroupTheory[IsTransitive]

 


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