Cayley table [SEP] named after
Cayley table
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 groupsuch as whether or not it is abelian, which elements are inverses of which elements, and the size and contents of the group's centercan be discovered from its Cayley table.
A simple example of a Cayley table is the one for the group {
table is in fact arbitrary, it is convenient to order them in the following manner: beginning with the group's identity element, which is always its own inverse, list first all the elements that are their own inverse, followed by pairs of inverses listed adjacent to each other.
Then, for a finite group of a particular order, it is easy to characterize its "identity skeleton", so named because the identity elements on the Cayley table are clustered about the main diagonaleither they lie directly on it, or