Order of a Group- Abstract Algebra

Finite and infinite Groups:

            If a group contains a finite number of distinct elements, it is called finite group otherwise an infinite group.
In other words, a group  is said to be finite or infinite according as the underlying set G is finite or infinite.

Order of a Group:

            The number of elements in a finite group is called the order of the group. An infinite group is said to be of infinite order.

Note: It should be noted that the smallest group for a given composition is the set consisting of the identity element  alone. 
Example:

• ,  is the example of finite group with order 3.
• ,  is the another example of finite group with order 4.