A Cayley table, after the 19th century British mathematician Arthur Cayley, 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 easily deduced by examining 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 |
Read more about Cayley Table: History, Structure and Layout, Constructing Cayley Tables, Permutation Matrix Generation, Generalizations
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