GroupTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : GroupTheory/CayleyTable

GroupTheory

  

CayleyTable

  

construct the Cayley table of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

CayleyTable( G )

CayleyTable( G, elements = E )

Parameters

G

-

a small group

E

-

(optional) list ; an ordering of the elements of G

Description

• 

The Cayley table of a (small) group G specifies the binary operation that defines G.

• 

The CayleyTable( G ) command returns the Cayley table of the group G, in which the elements of G have been labeled by the integers 1..n, where n is the order of G.

• 

If G is a group originally specified by its Cayley table, then the CayleyTable command simply returns it.  For other groups, the Cayley table is computed, if possible.

• 

You can specify a particular ordering for the elements of the group by passing the optional argument elements = E, where E is an explicit list of the members of G.

• 

The DrawCayleyTable command allows you to visualize the Cayley table of a small group using colors and can be formatted by using a wide variety of options.

• 

Note that computing the Cayley table of a group requires that all the group elements be computed explicitly, so the command should only be used for groups of modest size.

Examples

withGroupTheory:

GSymmetricGroup3

GS3

(1)

CayleyTableG

123456214365351624462513536142645231

(2)

Generate all elements of G using the combinat package.

permutation_listscombinat:-permute3

permutation_lists1,2,3,1,3,2,2,1,3,2,3,1,3,1,2,3,2,1

(3)

Translate these elements into their Group Theory representation.

permutationsmapPerm,permutation_lists

permutations,2,3,1,2,1,2,3,1,3,2,1,3

(4)

Get the CayleyTable of G where the elements are ordered as in the list permutations.

CayleyTableG,elements=permutations

123456214365351624462513536142645231

(5)

Compatibility

• 

The GroupTheory[CayleyTable] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

combinat[permute]

convert

GroupTheory

GroupTheory[CayleyTableGroup]

GroupTheory[DrawCayleyTable]

GroupTheory[SymmetricGroup]

map

with