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April 28th, 2013, 09:16 AM  #1 
Newbie Joined: Apr 2013 Posts: 1 Thanks: 0  isomorphic Subgroups of an infinite cyclic Group
Hey, Im trying to solve the folowing problem: Let G = <g> be a infinite cyclic group and H,N subgroups of G with H ? N. Then H = N. My Idea is that G is isomorphic to Z and the same isomorphism that proof this () should do the same with H and N: f(H)= f(N) = mZ for the right Is this right? I already checked the finite case. Thats easy. I only have a problem with this case. Greetings. 
April 28th, 2013, 01:51 PM  #2  
Senior Member Joined: Aug 2012 Posts: 2,384 Thanks: 743  Re: isomorphic Subgroups of an infinite cyclic Group Quote:
 

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cyclic, group, infinite, isomorphic, subgroups 
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