Abstract Algebra IBL Wiki

====== $HK$ 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 $HK=KH$. ---- ==== 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. ---- ==== $\LaTeX$ 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> ---- ==== External links ==== * {{tag>theorem ben needsreview rben}}