# Math Help - extension

1. ## extension

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

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

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

2. ## Re: extension

Originally Posted by vernal

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 $\alpha,\beta\gamma$?

3. ## Re: extension

Originally Posted by Drexel28
Something seems a little fishy here. Why do we need $\alpha,\beta\gamma$?
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