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 [math]\displaystyle{ \frac{G}{\ker \phi} }[/math] is normal in [math]\displaystyle{ \frac{G}{G'} }[/math]? The wording of this question is a little unclear to me.

-James

Answer. More fully, you have to show that given any group homomorphism [math]\displaystyle{ \phi:G\to A }[/math], where [math]\displaystyle{ A }[/math] is an Abelian group, there exists a group homomorphism [math]\displaystyle{ \bar\phi:G/G'\to A }[/math] such that [math]\displaystyle{ \phi=\bar\phi\circ\pi }[/math], where [math]\displaystyle{ \pi }[/math] is the projection [math]\displaystyle{ \pi:G\to G/G' }[/math]. (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)