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Matematicheskie Trudy, 2013, Volume 16, Number 1, Pages 28–55 (Mi mt248)  

This article is cited in 1 scientific paper (total in 1 paper)

On the space $\operatorname{Ext}$ for the group $SL(2,q)$

V. P. Burichenko

Institute of Mathematics, National Academy of Sciences of the Republic of Belarus, Gomel, Belarus
Full-text PDF (314 kB) Citations (1)
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Abstract: We consider the space $\operatorname{Ext}^r(A,B)=\operatorname{Ext}^r_{KG}(A,B)$, where $G=SL(2,q)$, $q=p^n$, $K$ is an algebraically closed field of characteristic $p$, $A$ and $B$ are irreducible $KG$-modules, and $r\geq1$. Carlson [6] described a basis of $\operatorname{Ext}^r(A,B)$ in arithmetical terms. However, there are certain difficulties concerning the dimension of such a space. In the present article, we find the dimension of $\operatorname{Ext}^r(A,B)$ for $r=1,2$ (in the above-mentioned article, Carlson presents the corresponding assertions without proofs; moreover, there are errors in their formulations). As a corollary, we find the dimension of the space $H^r(G,A)$, where $A$ is an irreducible $KG$-module. This result can be used in studying nonsplit extensions of $L_2(q)$.
Key words: finite simple groups, cohomologies, nonsplit extensions.
Received: 23.11.2012
English version:
Siberian Advances in Mathematics, 2014, Volume 24, Issue 2, Pages 100–118
DOI: https://doi.org/10.3103/S1055134414020023
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: V. P. Burichenko, “On the space $\operatorname{Ext}$ for the group $SL(2,q)$”, Mat. Tr., 16:1 (2013), 28–55; Siberian Adv. Math., 24:2 (2014), 100–118
Citation in format AMSBIB
\Bibitem{Bur13}
\by V.~P.~Burichenko
\paper On the space $\operatorname{Ext}$ for the group~$SL(2,q)$
\jour Mat. Tr.
\yr 2013
\vol 16
\issue 1
\pages 28--55
\mathnet{http://mi.mathnet.ru/mt248}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3156672}
\elib{https://elibrary.ru/item.asp?id=19000371}
\transl
\jour Siberian Adv. Math.
\yr 2014
\vol 24
\issue 2
\pages 100--118
\crossref{https://doi.org/10.3103/S1055134414020023}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические труды Siberian Advances in Mathematics
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    Abstract page:350
    Full-text PDF :81
    References:60
    First page:7
     
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