January 21st, 2014, 09:14 AM  #1 
Senior Member Joined: Nov 2011 Posts: 250 Thanks: 3  direct product
How can I prove that direct product of two groups is group? Or it did not?

January 21st, 2014, 11:52 AM  #2 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: direct product
Depending on how you define the binary operator.

January 22nd, 2014, 10:20 AM  #3 
Senior Member Joined: Nov 2011 Posts: 250 Thanks: 3  Re: direct product
I need to determine a direct prodcut binary operation that operate and if is possible direct product that doesn't operate or vice versa. Tell me  I don't know how to do it. May one look on it and tell me how to deal with it. Thanks, for the responders. 
January 22nd, 2014, 10:47 AM  #4 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: direct product
If you are given two groups with binary operations (G, g) and (H, h) use the binary operator over G x H as (g, h). You have a group then.

January 22nd, 2014, 12:05 PM  #5 
Senior Member Joined: Nov 2011 Posts: 250 Thanks: 3  Re: direct product
I don't understand which opeartion you decide to use? What is the operation you choose? I think you choose operation of Cartesain product? But what is the result? (I think it's a point). Please someone expand and explain the operation that operate here. Thanks and Bless you. 
January 22nd, 2014, 05:30 PM  #6  
Senior Member Joined: Aug 2012 Posts: 2,393 Thanks: 749  Re: direct product Quote:
(g, h) * (g', h1') = (gg', hh') where gg' is defined by the group operation on G; and hh' is defined by the group operation on H.  
January 23rd, 2014, 10:28 AM  #7 
Senior Member Joined: Nov 2011 Posts: 250 Thanks: 3  More question:
I have a more question: What is the identity element of the operating group result? Thanks for the guys who help me. How I find the identity element? 
January 23rd, 2014, 06:34 PM  #8 
Senior Member Joined: Mar 2012 Posts: 294 Thanks: 88  Re: direct product
The identity of GxH is the pair: where each of these is the identity element in their respective groups. 

Tags 
direct, product 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Direct Proof?  jrklx250s  Real Analysis  3  December 3rd, 2011 03:58 AM 
external direct product  Lila  Abstract Algebra  1  May 7th, 2011 08:43 AM 
Direct product of cyclic groups  SonicYouth  Abstract Algebra  10  March 23rd, 2011 08:10 AM 
Direct proportion  MathematicallyObtuse  Algebra  4  January 15th, 2011 07:26 PM 
Direct product  gianni  Abstract Algebra  2  December 2nd, 2010 05:00 AM 