extension

**vernal** · Dec 26th 2011, 08:39 AM

please help me.

if e is a free presentation of the group Q , and

${e}:N\stackrel{{\chi}}\longrightarrow{~~{G}}~\stackrel{{\pi}}\twoheadrightarrow~{Q}\nonumber\\~~~~~~~{{\alpha}}\downarrow~~~~~~~{{\beta}}\downarrow~~~{{\gamma}}\downarrow\\ ~~~~~~{e}:N\stackrel{{\chi}}\longrightarrow{~~{G}}~\stackrel{{\pi}}\twoheadrightarrow ~~{Q}$

$if~ \gamma={1}_Q~ then~ \frac{\chi N\cap[G,G]}{[\chi N,G]}=???$

**Drexel28** · Dec 28th 2011, 12:35 AM

Originally Posted by vernal

please help me.

if e is a free presentation of the group Q , and

${e}:N\stackrel{{\chi}}\longrightarrow{~~{G}}~\stackrel{{\pi}}\twoheadrightarrow~{Q}\nonumber\\~~~~~~~{{\alpha}}\downarrow~~~~~~~{{\beta}}\downarrow~~~{{\gamma}}\downarrow\\ ~~~~~~{e}:N\stackrel{{\chi}}\longrightarrow{~~{G}}~\stackrel{{\pi}}\twoheadrightarrow ~~{Q}$

$if~ \gamma={1}_Q~ then~ \frac{\chi N\cap[G,G]}{[\chi N,G]}=???$

Something seems a little fishy here. Why do we need $\displaystyle \alpha,\beta\gamma$?

**vernal** · Dec 28th 2011, 07:07 AM

Originally Posted by Drexel28

Something seems a little fishy here. Why do we need $\displaystyle \alpha,\beta\gamma$?

I don't know!!! I asked why. I saw this in the article. And I think is دnot related to alpha beta gamma.Maybe I did not understand the article.thanks

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