A Cayley table for a group is essentially the “multiplication table” of the group.11A caveat to novices in group theory: multiplication is usually used notationally to represent the group operation, but the operation needn’t resemble multiplication in the reals. Hence, you should take “multiplication table” with a grain or two of salt. The columns and rows of the table (or matrix) are labeled with the elements of the group, and the cells represent the result of applying the group operation to the row-th and column-th elements.
Formally, let be our group, with operation the group operation. Let be the Cayley table for the group, with denoting the element at row and column . Then
where is the th element of the group, and is the th element.
The Cayley table for , the permutation group of order 3, is
|Date of creation||2013-03-22 13:06:44|
|Last modified on||2013-03-22 13:06:44|
|Last modified by||akrowne (2)|