My Math Forum  

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

Abstract Algebra Abstract Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 10th, 2008, 08:57 AM   #1
Newbie
 
Joined: Dec 2008

Posts: 9
Thanks: 0

pls quickly answer ma quest about sylow thm

1. Let p be prime, and G be a finite group. If every element of G has order a power of p, then |G| = p^n for some n?0. (Hint: Use Cauchy’s theorem.)


2. Tell as much as possible about the subgroups of a group of order 30 and of a group of order 40.



3. Let G be a finite p-group and H<G. Prove that H<N G(H) .



please help me quickly... ? dont understand these ques.s
bogazichili is offline  
 
December 10th, 2008, 11:04 AM   #2
Senior Member
 
Joined: Nov 2008

Posts: 199
Thanks: 0

Re: pls quickly answer ma quest about sylow thm

for 1 suppose the order (size) of G is not a power of p. Then there must exist a prime q dividing the order of G such that q is not equal to p (by the fundamental theorem of arithmetic). By cauchy's theorem this means G has an element with order q. This is a contradiction as we are told that every element of G has order a power of p. As q is a prime distinct from p this cannot happen.
pseudonym is offline  
December 10th, 2008, 03:58 PM   #3
Member
 
Joined: Aug 2008

Posts: 84
Thanks: 0

Re: pls quickly answer ma quest about sylow thm

(3) is true in general (for any group). H always normalizes itself--this is not hard to see.
Spartan Math is offline  
December 12th, 2008, 01:50 AM   #4
Newbie
 
Joined: Dec 2008

Posts: 9
Thanks: 0

Re: pls quickly answer ma quest about sylow thm

Quote:
Originally Posted by Spartan Math
(3) is true in general (for any group). H always normalizes itself--this is not hard to see.
im new in this area so i do not understand easily.. may u pls explain detailly.
bogazichili is offline  
December 12th, 2008, 01:51 AM   #5
Newbie
 
Joined: Dec 2008

Posts: 9
Thanks: 0

Re: pls quickly answer ma quest about sylow thm

Quote:
Originally Posted by pseudonym
for 1 suppose the order (size) of G is not a power of p. Then there must exist a prime q dividing the order of G such that q is not equal to p (by the fundamental theorem of arithmetic). By cauchy's theorem this means G has an element with order q. This is a contradiction as we are told that every element of G has order a power of p. As q is a prime distinct from p this cannot happen.
thank you for ur attention... it s really help me to understand how ? can solve the quest.
bogazichili is offline  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
answer, pls, quest, quickly, sylow, thm



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
TOUGH QUEST.. MathMonster Number Theory 2 June 29th, 2013 05:07 AM
prob quest Kinroh Algebra 1 July 4th, 2012 02:05 PM
A Quest to Solve One of Math's Great Puzzles zombal Number Theory 4 April 29th, 2012 05:53 PM
Computing the rank of this matrix quickly? forcesofodin Linear Algebra 3 April 16th, 2010 01:30 PM
please help quickly about sylow thm and group action quest bogazichili Algebra 1 December 13th, 2008 07:13 AM





Copyright © 2017 My Math Forum. All rights reserved.