Talk:11-1100/Homework Assignment 1: Difference between revisions
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=== On II-3 === |
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"...that any morphism from G into an Abelian group factors through G / G' " |
"...that any morphism from G into an Abelian group factors through G / G' " |
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Is this just another way of asking to show that |
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. |
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-James |
-James |
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'''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) |
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Latest revision as of 08:34, 2 October 2011
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)
