Thread: Order of element

Let G be a finite group. Prove the order of any element v (which v is an element of G) divides the order |G|of G.

Originally Posted by apple2009

Let G be a finite group. Prove the order of any element v (which v is an element of G) divides the order |G|of G.

Hint: is a subgroup of . Now apply Lagrange's theorem.

am I need to prove v is a subgroup of G? and how?

Originally Posted by apple2009

am I need to prove v is a subgroup of G? and how?

You already know that is a subgroup of (or you should). Now use the fact that and Lagranges theorem.