Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
    
The given overgroup $\,G\,$ is abelian so all its subgroups are normal... –  DonAntonio Oct 17 '12 at 18:37

1 Answer 1

up vote 2 down vote accepted

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

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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