My Math Forum  

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

Abstract Algebra Abstract Algebra Math Forum

LinkBack Thread Tools Display Modes
September 28th, 2007, 10:22 AM   #1
Joined: Sep 2007

Posts: 9
Thanks: 0

finite group

Let G be a finite group of even order. Prove that G contains at least one element of order 2 ( that is, some c different from e with c^2=e).
stf123 is offline  
September 28th, 2007, 01:08 PM   #2
Global Moderator
Joined: Dec 2006

Posts: 20,099
Thanks: 1905

If p is any element other than e that's its own inverse, p = p^-1, so p² = e, so p is of order two.

There's an even number of elements which are not their own inverse, since they can be counted in pairs, each one paired with its inverse. There's therefore (since the group is of even order) an even number of elements which are their own inverse. The identity, e, is one, so there are an odd number of others, each being of order two.
skipjack is offline  

  My Math Forum > College Math Forum > Abstract Algebra

finite, group

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
example of a finite group.... rayman Abstract Algebra 7 March 4th, 2012 06:41 AM
Prove that this finite set is a group nata Abstract Algebra 2 October 30th, 2011 06:29 PM
Let G be a finite group and h:G>G an isomorphism, such that johnmath Abstract Algebra 2 November 27th, 2010 11:52 PM
when is this factor/quotient group finite? aptx4869 Abstract Algebra 0 September 26th, 2007 02:27 AM
T'-group finite (help-me please thanks) sastra81 Abstract Algebra 1 January 9th, 2007 08:05 AM

Copyright © 2019 My Math Forum. All rights reserved.