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
May 25th, 2017, 08:59 AM   #1
Newbie
 
Joined: Aug 2013

Posts: 16
Thanks: 0

Suppose G is a group, a ∈ G and H is a subgroup of G.

1. Show that aH and H have the same cardinality by exhibiting a bijection between the two sets. (Similarly, one can show that Ha and H have the same cardinality, so aH and Ha always have the same cardinality.)

I've never actually demonstrated bijections between cosets and subgroups before, how would I go about this?

2. Show, by means of an example, that aH is not necessarily equal to Ha. (Hint: it has to be a non-commutative group.)

Would any non-commutative group work for this? Apologies, I can't get my intuition around for this problem
facebook is offline  
 
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
, cosets, group, subgroup, suppose



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Group and subgroup ordering Linda2 Abstract Algebra 1 March 31st, 2012 12:39 PM
let G be p-group then every subgroup H, |H| = p, is normal s johnmath Abstract Algebra 3 March 3rd, 2011 09:22 AM
Subgroup of Abelian Group LoveOneAnother Abstract Algebra 1 November 7th, 2010 05:37 AM
Subgroup/Normal Subgroup/Factor Group Questions envision Abstract Algebra 1 October 4th, 2009 04:24 AM
subgroup pronormal and T-group sastra81 Abstract Algebra 1 January 3rd, 2007 08:58 AM





Copyright © 2017 My Math Forum. All rights reserved.