1. ## [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.

2. To show that $aH\subset Ha$, 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 $ah$ for some $h\in H$. And since $ah=ha$, ...

3. Thanks Bruno, I figured it out.