(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If H is a subgroup of a finite group G, and if the order of G is m times the order of H, |G|=m|H|, adapt the proof of Lagrange's theorem to show that g^{m!}is an element of H for all g in G.

3. The attempt at a solution

My thoughts so far were to think that we can divide G into m pieces: H, g_{1}H, g_{2}H, ..., g_{m-1}H. If we now take an arbitrary g_{k}, it is certainly in g_{k}H, since H contains the identity. The question now is: what happens if we look at g_{k}^{2}, (g_{k}^{2})^{3}... where do they end up? I need a hint...

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# Question about Lagranges theorem in Group Theory

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