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.