Let G be a finite group, let H be a subgroup of G and let N be a normal subgroup of G. Show that if |H| and |G:N| are relatively prime then H is a subgroup of N.(adsbygoogle = window.adsbygoogle || []).push({});

I have tried using the fact that since N is normal, HN is a subgroup of G.

Suposing that H is not contained in N, I tried finding a common factor for |H| and |G:N|.

Numbers that divide |H| are |HnN|, |HnN| and |H|.

Numbers that divide |G:N| are |GN| and |HN:N|.

I'm stuck.

I would appreciate any suggestions.

Thanks

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# Show H is a subgroup of N

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