# Cayley table

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 $G$ be our group, with operation $\circ$ the group operation. Let $C$ be the Cayley table for the group, with $C(i,j)$ denoting the element at row $i$ and column $j$. Then

 $C(i,j)=e_{i}\circ e_{j}$

where $e_{i}$ is the $i$th element of the group, and $e_{j}$ is the $j$th element.

## 0.1 Examples.

Title Cayley table CayleyTable 2013-03-22 13:06:44 2013-03-22 13:06:44 akrowne (2) akrowne (2) 11 akrowne (2) Definition msc 20A99 Cayley-table