Is this statement true? I'm guessing it's obvious, but I don't see why.
If two groups are isomorphic, then one is finitely generated iff the other is.
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$\begingroup$
abstract-algebra
group-theory
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2If $\varphi : G \to G'$ is an isomorphism, then go to the definition of "finitely generated" and insert a bunch of $\varphi$s and $\varphi^{-1}$s. – 2012-11-11
1 Answers
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The image under an isomorphism of a set of generators of one group is a set of generators of the other.
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2And the inverse of an isomorphism is again an isomorphism. – 2012-11-11