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.
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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 $\displaystyle k\in G'$ then $\displaystyle k\varphi(N)k^{-1}=\varphi(N)$, but $\displaystyle k=\varphi(n)$ for some $\displaystyle n$....so? P.S. Nice name.
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