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Let G be group; let H and K be subgroups of G, with a normal subgroup of G. Prove every member of the quotient group HK/H may be written in the form Hk for some k in K. Not sure what to even do with this?

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If $H$ is a normal subgroup of G then $gH=Hg\quad \forall g \in G$

The quotient group of $HK/H$ is defined as {$hkH $ | $hk \in HK$} but as H is a normal subgroup this is equal to {$Hhk $ | $hk \in HK$} and $Hh$ = $H$ as H is a subgroup and therefore closed under multiplication as $h \in H$

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