construct a permutation group isomorphic to a special orthogonal group
SpecialOrthogonalGroup(d, n, q)
0, 1 or -1
a positive integer
power of a prime number
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:
G ≔ SpecialOrthogonalGroup⁡1,4,7
G ≔ SO4,7
G ≔ SpecialOrthogonalGroup⁡−1,4,7
The GroupTheory[SpecialOrthogonalGroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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