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

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==== Remarks ==== 
  * See problem [[problem:exploring_the_set_products_hk_and_kh_on_d4]] to have the students conjecture this theorem before having them prove it. 


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==== $\LaTeX$ version ====
<file tex 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}
</file>

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==== External links ====
  * 

{{tag>theorem ben needsreview rben}}