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

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


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)
References:
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}
Linking options:
  • https://www.mathnet.ru/eng/mt248
  • https://www.mathnet.ru/eng/mt/v16/i1/p28
  • 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
    Statistics & downloads:
    Abstract page:349
    Full-text PDF :81
    References:60
    First page:7
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024