1. ## Abelian subgroup proof

If X, Y are subgroups of abelian group G, show XY={xy|xinX and yinY} is also subgroup of G.

Would really appreciate some help with this.

2. Originally Posted by tamiani
If X, Y are subgroups of abelian group G, show XY={xy|xinX and yinY} is also subgroup of G.

Would really appreciate some help with this.
Remember how we prove a subgroup. We need to show $a,b\in XY$ then $ab \in XY$. You also need to show $e\in XY$. Any if $a\in XY$ then $a^{-1} \in XY$. Can you do these things? They should be straightforward.

3. I thought that was it, but it seemed too simple. Thanks lots