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

Let P be a p-sylow sbgrp of a finite group G.

N(P) will be the normalizer of P in G. The quotient group N(P)/P is cyclic from order n.

PROVE that there is an element a in N(P) from order n and that every element such as a represnts a generator of the quotient group N(P)/P

2. Relevant equations

3. The attempt at a solution

Welll.... there is mP in N(P)/P such as (mP)^n = P -> m^n*P=P -> m^n = 1 ...

If m has order that is less the n, we'll get a contradiction to the fact that mP is from order n.

It's pretty obvious that every element of this kind is a generator of this group...But I realy feel I'm missing something... It's a 20 points question and the answer will take me 2 lines...

Where is my mistake?

TNX in advance

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# Homework Help: Abstract->p-sylow groups

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