My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum

LinkBack Thread Tools Display Modes
November 3rd, 2011, 06:05 PM   #1
Joined: Oct 2011

Posts: 2
Thanks: 0

Herstein: Abstract Algebra Proof (Sylow's Theorem)

if P^m divides |G|, show that G has a subgroup of order P^m
ThatPinkSock is offline  
November 11th, 2011, 04:25 AM   #2
Joined: Jun 2010

Posts: 64
Thanks: 0

Re: Herstein: Abstract Algebra Proof (Sylow's Theorem)

We have to solve it by sylow theorem,
P^m divides |G| then we have that p||G|,so exist an integer n such that P^n| |G| and n is the greatest
integer that P^n||G|, By the sylow theorem exist a subgroup H<G with order P^n.
so H is p-group (p is simple)
We have that m<=n;
you have to find a subgroup D<H<G that the order of |D|=p^m
The existence of the group D is guaranted by a theorem in p-group.
Use this theorem below
Theorem: if G(in your case H) is a group of order p^n, then exist a subgroup D of G
with order p^i , for i=1,2,,,,,m-1,m

This theorem guaranted the existence of a subgroup H with order p^m (m<=n)

Note : In your question you have to add that p-is prime,.becouse in general
is not true that "for p not prime,and P^m divides |G|, show that G has a subgroup of order P^m , ,"
johnmath is offline  

  My Math Forum > College Math Forum > Abstract Algebra

abstract, algebra, herstein, proof, sylow, theorem

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Sylow Theorem dpsmith Abstract Algebra 2 April 8th, 2014 03:51 AM
Abstract Algebra Help MastersMath12 Abstract Algebra 1 September 24th, 2012 11:07 PM
Abstract Algebra-p-sylow groups WannaBe Abstract Algebra 0 December 22nd, 2009 10:34 AM
Abstract Algebra - Proof involving groups Jamers328 Abstract Algebra 15 October 29th, 2008 12:21 PM
Abstract Algebra Proof - Form of a^2, a an integer karasuman Abstract Algebra 9 August 13th, 2008 02:01 PM

Copyright © 2017 My Math Forum. All rights reserved.