what is cayleys table?

Question

explanation only

Answer 1

A cayley table is just like a multiplication table for a group. You write all the group elements across the top, and again down the left, and what each pair multiply to in the middle.

Answer 2

Given a set of n elements x1, ..., xn, with a binary operation ("composition", "multiplication", etc.), we can represent the operation by a Cayley table. This is an n x n array with (i,j) entry xi o xj, where o denotes the binary operation. Sometimes we take the entry to be the index k for which xi o xj = xk.