Subset Product of Abelian Subgroups

Theorem
Let $$\left({G, \circ}\right)$$ be an abelian group.

Let $$H_1$$ and $$H_2$$ be subgroups of $$G$$.

Then $$H_1 \circ H_2$$ is a subgroup of $$G$$.

Proof
From All Subgroups of Abelian Group are Normal, $$H_1$$ and $$H_2$$ are normal.

The result follows from Subgroup Product with Normal Subgroup is Subgroup‎.