# Math Help - Order of element

1. ## 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.

2. 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: $\langle v\rangle$ is a subgroup of $G$. Now apply Lagrange's theorem.

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

4. Originally Posted by apple2009
am I need to prove v is a subgroup of G? and how?
You already know that $\langle v\rangle$ is a subgroup of $G$ (or you should). Now use the fact that $|v|=|\langle v\rangle|$ and Lagranges theorem.