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TheForumLord
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Homework Statement
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
Homework Equations
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 really 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