The multiplication table for a group. Given a finite group G = {g1,…gn}, then the product gigj appears in the ith row and jth column of the table. As pre-multiplication by gi and post-multiplication by gj are both invertible, then a Cayley table is a Latin square.
A tabular means of describing a finite group, first used by the 19th-century mathematician Arthur Cayley. To illustrate, the set
forms a group under the dyadic operation ° as described by the Cayley table shown in the diagram. The value of −1°i, for example, is −i. The name composition table is usually used when the group operation is composition of functions.
Cayley table.
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