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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 = 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 ($f: n*g \rightarrow n$) should do the same with H and N: f(H)= f(N) = mZ for the right $m \in Z$ 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
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Re: isomorphic Subgroups of an infinite cyclic Group

Quote:
 Originally Posted by Belov Hey, Im trying to solve the folowing problem: Let G = be a infinite cyclic group and H,N subgroups of G with H ? N. Then H = N.
G = Z (additive group of integers), H = <2> and N = <3> is a counterexample.

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