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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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  • $\begingroup$ @DietrichBurde edited $\endgroup$ – openspace Sep 20 '17 at 20:37
  • $\begingroup$ Is it not the other way around, i.e., $[G:K]\mid k!$? $\endgroup$ – Dietrich Burde Sep 20 '17 at 20:40

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