Matematicheskie Trudy
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Tr.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Tr., 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

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.

Full text: PDF file (314 kB)
References: PDF file   HTML file

English version:
Siberian Advances in Mathematics, 2014, 24:2, 100–118

Bibliographic databases:

UDC: 512.542
Received: 23.11.2012

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://www.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}


Linking options:
  • http://mi.mathnet.ru/eng/mt248
  • http://mi.mathnet.ru/eng/mt/v16/i1/p28

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. P. Burichenko, “Nonsplit extensions of Abelian $p$-groups by $L_2(p^n)$ and general theorems on extensions of finite groups”, Siberian Adv. Math., 25:2 (2015), 77–109  mathnet  crossref  mathscinet
  • Математические труды Siberian Advances in Mathematics
    Number of views:
    This page:238
    Full text:59
    References:39
    First page:7

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022