November 7th, 2010, 10:08 AM  #1 
Newbie Joined: Dec 2009 Posts: 7 Thanks: 0  Isomorphic
Suppose m, n are positive integers which are coprime. Show that U_n X U_m is isomorphic to U_mn. What is the function that maps U_n X U_m to U_mn? Thx! 
November 12th, 2010, 10:42 AM  #2 
Site Founder Joined: Nov 2006 From: France Posts: 824 Thanks: 7  Re: Isomorphic
There's not necessarily only one such function. Naturally, such a function maps a generator of U_n x U_m, for instance (e^(2iPi/m),e^(2iPi/n)), onto a generator of U_(mn), for instance e^(2iPi/(mn)). (Proof: use the fact that both sets have same cardinal, thus it is enough to prove that such a function is a group endomorphism and is injective). 

Tags 
isomorphic 
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 
isomorphic normal extensions  Epsilon90  Abstract Algebra  4  November 28th, 2013 01:49 AM 
Let G be a group of order 24 that is not isomorphic to S4...  Artus  Abstract Algebra  1  August 1st, 2013 06:45 AM 
Show two groups are nonisomorphic.  watson  Abstract Algebra  8  January 12th, 2013 05:03 PM 
(Q, +) not isomorphic with (Q*, x)  Kappie  Abstract Algebra  9  March 5th, 2012 12:53 PM 
Isomorphic Groups..U(8) and Z4  jcrot30  Abstract Algebra  5  March 31st, 2011 08:51 AM 