Next we give two examples of finite groups. For a finite group we denote by the number of elements in . A finite group can be given by its multiplication table (also called the Cayley table). This is a square table of size ; the rows and columns are indexed by the elements of ; the entry in the row and column is .
We are now going to list some basic consequences of our defining axioms for groups.
First of all, we note that associativity implies that
in a product of any number of elements
in that order, the arrangement of brackets does not matter.
For example, we have
Edmund F Robertson
11 September 2006