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.

I'm trying to prove If $f:G\to H$ is a homomorphism with Kernel $N$ and $K\lt G$, then $f^{-1}(f(K))=KN$.

Since $N$ is a normal subgroup of G, I know that $N\cap K$ is a normal subgroup of $K$ and $NK=N\vee K=KN$, but I don't how to go further, I need help.

Thanks in advance

share|improve this question

1 Answer 1

Trying thinking about why $f^{-1}(f(K))= KN$ makes sense (What is $f^{-1}(e_H)$?).

Another thing to think about is what the elements in a particular coset $aN$ have in common with each other (If $a,b\in G$ and $aN=bN$, is there a relation between $a$ and $b$'s image under $f$?).

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.