Back جدول كايلي Arabic Taula de Cayley Catalan Cayleyho tabulka Czech Verknüpfungstafel German Kejlia tabelo Esperanto Tabla de Cayley Spanish جدول کیلی Persian Table de Cayley French טבלת קיילי HE Tabella de Cayley Interlingua
Named after the 19th century British mathematician Arthur Cayley, a Cayley table describes the structure of a finite group by arranging all the possible products of all the group's elements in a square table reminiscent of an addition or multiplication table. Many properties of a group – such as whether or not it is abelian, which elements are inverses of which elements, and the size and contents of the group's center – can be discovered from its Cayley table.
A simple example of a Cayley table is the one for the group {1, −1} under ordinary multiplication:
| × | 1 | −1 |
|---|---|---|
| 1 | 1 | −1 |
| −1 | −1 | 1 |