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GroupTheory

  

MinimumPermutationRepresentationDegree

  

compute the minimum degree of a permutation representation of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

MinimumPermutationRepresentationDegree( G )

MinPermRepDegree( G )

Parameters

G

-

a group

Description

• 

Cayley's Theorem asserts that each finite group is isomorphic to a group of permutations of a finite set.  In other words, each finite group G can be embedded in a symmetric group Sn, for some positive integer n.

• 

The MinimumPermutationRepresentationDegree( G ) command returns the minimum degree of a faithful permutation representation for a (finite) group G.  That is the least positive integer n such that G embeds in the symmetric group of degree n.

• 

You can use the alias MinPermRepDegree instead of the longer command name MinimumPermutationRepresentationDegree.

Examples

withGroupTheory:

MinPermRepDegreeCyclicGroup12

7

(1)

MinPermRepDegreeGL2,5

24

(2)

MinPermRepDegreeQuaternionGroup

8

(3)

MinPermRepDegreePSL5,q

q4+q3+q2+q+1

(4)

Compatibility

• 

The GroupTheory[MinimumPermutationRepresentationDegree] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

GroupTheory

GroupTheory[CyclicGroup]

GroupTheory[GL]

GroupTheory[SymmetricGroup]