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March 31st, 2010, 04:53 AM  #1 
Newbie Joined: Mar 2010 Posts: 3 Thanks: 0  size of Hom(Z,Z/2Z)
I have seen that there exists two group homomorphisms from Z to Z/2Z. However, I cannot seem to understand this. I mean I know that there exists a trivial grp hom. which sends all of Z to 0 in Z/2Z. But I cannot think of anymore. Any help?

April 2nd, 2010, 01:40 PM  #2 
Member Joined: Mar 2010 Posts: 32 Thanks: 0  Re: size of Hom(Z,Z/2Z)
Answered on physicsforums.com. (It's best if you have a satisfactory answer on another forum to say so in this forum to save duplication of effort.) 
April 3rd, 2010, 01:48 AM  #3 
Senior Member Joined: Dec 2009 Posts: 150 Thanks: 0  Re: size of Hom(Z,Z/2Z)
Map even numbers to zero, and odd ones to 1. No two even numbers can add to be odd, but odd numbers always add to be even, while odd + even or even + odd gives you an odd number. Compare this with adding 0 and 1 modulo 2.

April 3rd, 2010, 09:47 AM  #4 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: size of Hom(Z,Z/2Z)
Even though this has been answered, I'm moving it to the algbera section, where it fits better.


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