Consider a group $G$, and $H \in G$ - subgroup with $[G:H] = k$, then prove that there is exists normal subgroup $K$ in $H$ such that $k! | [G:K]$?
Actually I have no ideas. Any hints?
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@DietrichBurde edited – openspace Sep 20 '17 at 20:37
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Is it not the other way around, i.e., $[G:K]\mid k!$? – Dietrich Burde Sep 20 '17 at 20:40