Let G be a finite group with identity e. Suppose that a an element of G has order n. Show

that H = {e, a, a^2,...,a^n-1} is a subgroup of G.

supposedly first meant to show that a^m is an element of H for

any natural number m then use Lagrange's Theorem to deduce that the order of any

element must divide the order of the group.

im really stuck with this group theory work.. if someone could run through this it would be much appreciated!

thank you