GroupTheory
SymplecticGroup
construct a permutation group isomorphic to a symplectic group
Calling Sequence
Parameters
Description
Examples
Compatibility
SymplecticGroup(n, q)
Sp(n, q)
n
-
an even positive integer
q
power of a prime number
The symplectic group is the group of all matrices over the field with elements that respect a fixed nondegenerate symplectic form. The integer must be even.
The SymplecticGroup( n, q ) command returns a permutation group isomorphic to the symplectic group .
Note that for the groups and are isomorphic, so that a special linear group is returned in this case.
If either, or both, of n and q is non-numeric, then a symbolic group representing the symplectic group is returned.
The Sp( n, q ) command is provided as an abbreviation.
In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.
For the corresponding special linear group is returned.
Note the exceptional isomorphism:
The GroupTheory[SymplecticGroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
The GroupTheory[SymplecticGroup] command was updated in Maple 2020.
See Also
GroupTheory[AreIsomorphic]
GroupTheory[ClassNumber]
GroupTheory[Degree]
GroupTheory[Generators]
GroupTheory[GroupOrder]
GroupTheory[ProjectiveSymplecticGroup]
GroupTheory[SpecialLinearGroup]
GroupTheory[SymmetricGroup]
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