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April 28th, 2013, 09:16 AM   #1
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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.
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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 = <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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