2
$\begingroup$

Is this statement true? I'm guessing it's obvious, but I don't see why.

  • 2
    If $\varphi : G \to G'$ 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 1

5

The image under an isomorphism of a set of generators of one group is a set of generators of the other.

  • 2
    And the inverse of an isomorphism is again an isomorphism.2012-11-11