2
$\begingroup$

Suppose $(G,+,0)$ is an abelian group and $M,N\subseteq G$ two subsets.

Let $\langle M\rangle$ denotes the subgroup of $G$ generated by $M$ and let $\varphi:G\to G/\langle M\rangle$ denotes the quotient map.

Are $(G/\langle M\rangle)/\langle \varphi(N)\rangle$ and $G/\langle M\cup N\rangle$ isomorphic?

$\endgroup$
  • $\begingroup$ The given overgroup $\,G\,$ is abelian so all its subgroups are normal... $\endgroup$ – DonAntonio Oct 17 '12 at 18:37
2
$\begingroup$

You have obvious homomorphisms $[g]\to[g]$ in both directions, whose composition is of course the identity.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.