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 Subgroup of Abelian Group is Normal, $H_1$ and $H_2$ are normal.

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

$\blacksquare$