Let $H$ and $K$ be subgroups of a group $G$. Then $HK$ is a subgroup if and only if $HK=KH$.

• See problem exploring_the_set_products_hk_and_kh_on_d4 to have the students conjecture this theorem before having them prove it.

theorem.hk_is_a_subgroup_iff_hk_kh.tex

\begin{theorem}
Let $H$ and $K$ be subgroups of a group $G$. Then $HK$ is a subgroup if and only if $HK=KH$. 
\end{theorem}

theorem ben needsreview