Groups(part 3):

Oder of an element.

Let (G,*) be a multiplicative group and a is any element of G. Then a non-negative smallest integer n is said to be order of element a if

The order of the element a is denoted by o(a).
a is said to be of infinite order( or of order zero), if there doesn’t exist any positive integer n such that a^n=e.

Example.

1.

2.