GroupTheory
SpecialOrthogonalGroup
construct a permutation group isomorphic to a special orthogonal group
Calling Sequence
Parameters
Description
Examples
Compatibility
SpecialOrthogonalGroup(d, n, q)
SO(d, n, q)
d
-
0, 1 or -1
n
a positive integer
q
power of a prime number
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.
C
1a
2a
2b
2c
3a
3b
3c
3d
4a
4b
4c
4d
6a
6b
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6d
8a
8b
12a
12b
|C|
1
18
72
8
32
6
36
48
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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