construct the Cayley table of a group
CayleyTable( G )
CayleyTable( G, elements = E )
a small group
(optional) list ; an ordering of the elements of G
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.
G ≔ SymmetricGroup⁡3
Generate all elements of G using the combinat package.
permutation_lists ≔ combinat:-permute⁡3
Translate these elements into their Group Theory representation.
permutations ≔ map⁡Perm,permutation_lists
Get the CayleyTable of G where the elements are ordered as in the list permutations.
The GroupTheory[CayleyTable] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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