SymplecticGroup - Maple Help
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GroupTheory

  

SymplecticGroup

  

construct a permutation group isomorphic to a symplectic group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

SymplecticGroup(n, q)

Sp(n, q)

Parameters

n

-

an even positive integer

q

-

power of a prime number

Description

• 

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.

Examples

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

For  the corresponding special linear group is returned.

(15)

Note the exceptional isomorphism:

(16)

(17)

(18)

(19)

(20)

Compatibility

• 

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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