Cayley table
Mathematical tool in group theory / From Wikipedia, the free encyclopedia
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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:
More information ×, −1 ...
× | 1 | −1 |
---|---|---|
1 | 1 | −1 |
−1 | −1 | 1 |
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