Talk:11-1100/Homework Assignment 1

From Drorbn
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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)