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Math Help - isoclinism

  1. #1
    Member vernal's Avatar
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    isoclinism

    About isoclinism can put a book? I need it.

    who can solved this question?

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    Last edited by vernal; December 19th 2011 at 04:09 AM.
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  2. #2
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    Re: isoclinism

    Quote Originally Posted by vernal View Post
    About isoclinism can put a book? I need it.

    who can solved this question?

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    Here are notes my professor has on isoclinic:
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  3. #3
    Member vernal's Avatar
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    Re: isoclinism

    Quote Originally Posted by dwsmith View Post
    Here are notes my professor has on isoclinic:
    Tanks, but my order is as follow:


    Let \\<br />
{e}_i: {N}_i\overset{{\chi}_i }{\rightarrow}{G}_i\overset{{\pi}_i }{\rightarrow}{Q}_i\\<br />
central~ extensions.~ let~ us~ denote ~ by ~ c~ the~ commutator~ function~of~ e,~ i.e~\\<br />
c:~Q\times Q\rightarrow [G,G];~ (\pi g,\pi h)\rightarrow [g,h]\\<br />
the~ centeral ~ extensions ~ {e}_1 ~ and ~ {e}_2 ~ are~ called ~isoclinic,~ precisely~when~there~exist~isomorphisms~\eta :{Q}_1  \to  {Q}_2 ~~ and~ ~ \xi \zeta :[{G}_1,{G}_1] \to [{G}_2,{G}_2], Such ~that ~the~following~ diagram~ is~ commutative:~\\<br />
\\<br /> <br /> <br />
~~~{Q}_1\times {Q}_1 \overset{{C}_1}{\rightarrow}[{G}_1,{G}_1]\\<br />
\leftset{\eta \times \eta }\downarrow~~~~~~~~~\rightset{\xi }\downarrow\\<br />
~~~{Q}_2\times {Q}_2\overset{{c}_2}{\rightarrow}[{G}_2,{G}_2]\\<br /> <br />
\\<br /> <br />
i.e.~ \xi [{g}_1,{h}_1]=[{g}_2,{h}_2]~ for ~ all ~ {g}_1, {h}_1 belong~ to ~ {G}_1 ~, {\pi }_2{g}_2 = \eta {\pi }_1{g}_1, {\pi }_2{h}_2= \eta {\pi }_1{h}_1. ~The~ pair~ (\eta ,\xi )~ is ~called ~an~ isoclinism~ from~ {e}_1~ to~ {e}_2~,denote by (\eta ,\xi ): {e}_1\sim {e}_2 .<br /> <br />
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