Thread: [SOLVED] Proving subgroups

Hey guys,

I am stuck on the following problem:

If C is a subgroup of an abelian group G, then a*H = H*a for all a in G.

I know that I have to prove

1.) a*H is a subset of H*a

2.) H*a is a subset of a*H

After this, I really don't know how to go about it. Thanks for any and all help.

To show that , take any element on the left side and show that it's also an element of the right side. An element of the left side is for some . And since , ...

Thanks Bruno, I figured it out.