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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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