Order of Group

Let G be a finite group. Then the number of elements in G is called the order of the group G and is denoted by O(G) or |G|

Definition:

Let G be group and a ϵ G. IF there exists a positive integer n such that an = e, then the least such positive integer n is called the order of a.

If no such positive integer exists then we say that a is of infinite order.

Example:

G = { 1, -1, i, -I}

O(G) = 4


Let G be a group and a, b ϵ G with O(a) = 5, a^3b = ba^3 .Prove that G is an abelian group.


 

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