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Problem of the Week #297 - January 5, 2021

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Euge

MHB Global Moderator
Staff member
Jun 20, 2014
1,905
Here is this week's POTW:

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Let $G$ be a finite group, and let $H$ be a subgroup of $G$ of index $n$. Prove that if the order of $G$ does not divide $n!$, then $H$ contains a normal subgroup of $G$.

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