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 7th, 2011, 05:18 AM   #1
Newbie
 
Joined: May 2011

Posts: 1
Thanks: 0

external direct product

How do you prove that the external direct product of any finite number of groups is a group?
Lila is offline  
 
May 7th, 2011, 08:43 AM   #2
Senior Member
 
Joined: Jun 2010

Posts: 618
Thanks: 0

Re: external direct product

Lila,

The first thing is to define what the operation on the product is going to be. Of course, it is what you would expect---component-wise addition (or multiplication, depending on what notation you are using). The second is to show that this operation makes the set (product) closed under the operation, etc., i.e. it satisfies all the group axioms. To that end, if



and are written as



so that the operation is defined by



then you need to show that



-Ormkärr-
 is offline  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
direct, external, product



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
direct product shaharhada Abstract Algebra 7 January 23rd, 2014 06:34 PM
Mathematica help_NDsolver and external relations eride87 Applied Math 1 April 9th, 2013 06:31 AM
Direct product of cyclic groups SonicYouth Abstract Algebra 10 March 23rd, 2011 08:10 AM
Direct product gianni Abstract Algebra 2 December 2nd, 2010 05:00 AM
Direct Substitution? MathNoob Calculus 4 March 5th, 2009 06:18 AM





Copyright © 2019 My Math Forum. All rights reserved.