View source for 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>\frac{G}{\ker \phi}</math> is normal in <math>\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>\phi:G\to A</math>, where <math>A</math> is an Abelian group, there exists a group homomorphism <math>\bar\phi:G/G'\to A</math> such that <math>\phi=\bar\phi\circ\pi</math>, where <math>\pi</math> is the projection <math>\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). [[User:Drorbn|Drorbn]] 09:34, 2 October 2011 (EDT)