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March 31st, 2010, 04:53 AM   #1
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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?
jakelyon is offline  
April 2nd, 2010, 01:40 PM   #2
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Re: size of Hom(Z,Z/2Z)

Answered on

(It's best if you have a satisfactory answer on another forum to say so in this forum to save duplication of effort.)
Martin Rattigan is offline  
April 3rd, 2010, 01:48 AM   #3
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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.
forcesofodin is offline  
April 3rd, 2010, 09:47 AM   #4
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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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homz, size, z or 2z

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