A set G with an operation ◌ that meets the following requirements:
- ◌ is associative
- there is an element e in G such that a◌e = a and e◌a = a for all a in G
- for every a in G there is an element a¹ in G such that a◌a¹ = e and a¹◌a = e
is said to be a Group.
An example of a group is set of all integers with the operation of addition.
Groups have the property that:
-(ab)¹ = b¹a¹
-(a¹)¹=a
For a finite group the number of elements is contains is said to be its order
