My Math Forum $|H|$ is relatively prime to $[G:H]$

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 September 30th, 2017, 03:22 AM #1 Senior Member   Joined: Jan 2015 From: usa Posts: 104 Thanks: 1 $|H|$ is relatively prime to $[G:H]$ Ineed help to solve the following problem: Let $G$ be a finite group and $H  October 3rd, 2017, 10:23 AM #2 Member Joined: Jan 2016 From: Athens, OH Posts: 93 Thanks: 48 For p a prime, you just need to use 2 elementary properties of a finite p group P. 1. If Q is a proper subgroup of P,$Q\subset N_P(Q)$2. If$<1>\neq N$is a normal subgroup of P,$N\cap Z(P)\neq <1>$ Tags$gh$,$|h|\$, prime

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