Are they isomorphic?

Groups, Rings, Domains, Modules, etc, Galois theory
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Vangelis Mouroukos
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Former Team Member
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Are they isomorphic?

#1

Post by Vangelis Mouroukos »

Let \(G\) and \(H\) be groups such that there exist monomorphisms \(\varphi : G \longrightarrow H\) and \(\psi : H \longrightarrow G\). In each of the following cases, determine whether the groups \(G\) and \(H\) are isomorphic:

(a) \(G\) and \(H\) are abelian groups.

(b) \(G\) and \(H\) are finitely generated abelian groups.
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