Talk:11-1100/Homework Assignment 1

On II-3

"...that any morphism from G into an Abelian group factors through G / G' "

Is this just another way of asking to show that ${\frac {G}{\ker \phi }}$ is normal in ${\frac {G}{G'}}$? The wording of this question is a little unclear to me.

-James

Answer. More fully, you have to show that given any group homomorphism $\phi :G\to A$, where $A$ is an Abelian group, there exists a group homomorphism ${\bar {\phi }}:G/G'\to A$ such that $\phi ={\bar {\phi }}\circ \pi$, where $\pi$ is the projection $\pi :G\to G/G'$. (Sorry it took me long to respond, I was out of commission for much of last week and I'm only now getting better). Drorbn 09:34, 2 October 2011 (EDT)