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 $\displaystyle a,b\in XY$ then $\displaystyle ab \in XY$. You also need to show $\displaystyle e\in XY$. Any if $\displaystyle a\in XY$ then $\displaystyle a^{-1} \in XY$. Can you do these things? They should be straightforward.