# Homomorphism Proof.

• October 18th 2011, 04:09 PM
ThatPinkSock
Homomorphism Proof.
From Herstein's Abstract Algebra. Section 2.7 #7

If φ is a homomorphism of G onto G' and N ◅ G, show that φ(N) ◅ G.
• October 18th 2011, 04:14 PM
Drexel28
Re: Homomorphism Proof.
Quote:

Originally Posted by ThatPinkSock
From Herstein's Abstract Algebra. Section 2.7 #7

If φ is a homomorphism of G onto G' and N ◅ G, show that φ(N) ◅ G.

You want to prove that if $k\in G'$ then $k\varphi(N)k^{-1}=\varphi(N)$, but $k=\varphi(n)$ for some $n$....so?

P.S. Nice name.