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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 2, Pages 133–142 (Mi timm230)  

This article is cited in 9 scientific papers (total in 9 papers)

Automorphisms and normal structure of unipotent subgroups of finitary Chevalley groups

V. M. Levchuk, G. S. Suleimanova

Institute of Mathematics, Siberian Federal University
Full-text PDF (190 kB) Citations (9)
References:
Abstract: The description of the automorphisms of an unipotent subgroup $U$ of a Chevalley group over a field $K$ known earlier for $\operatorname{char}K\ne2,3$ (Gibbs, 1970) was completed in 1990 together with a solution of problem (1.5) from A. S. Kondrat’ev's survey (Usp. Mat. Nauk, 1986). In the present paper, $\operatorname{Aut}U$ is described for the case of finitary Chevalley groups. For a Chevalley group of classical type, it is proved that any large Abelian subgroup from $U$ is conjugate to a normal subgroup in $U$. It is shown that this is not so in the general case; therefore, problem (1.6) from Kondrat'ev's survey about large Abelian subgroups in $U$ is reduced to listing the exceptions. Large Abelian normal subgroups were listed by the authors earlier.
Keywords: finitary Chevalley group, unipotent subgroup, automorphism, large abelian subgroup.
Received: 19.01.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, Volume 267, Issue 1, Pages S118–S127
DOI: https://doi.org/10.1134/S0081543809070128
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: V. M. Levchuk, G. S. Suleimanova, “Automorphisms and normal structure of unipotent subgroups of finitary Chevalley groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 133–142; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S118–S127
Citation in format AMSBIB
\Bibitem{LevSul09}
\by V.~M.~Levchuk, G.~S.~Suleimanova
\paper Automorphisms and normal structure of unipotent subgroups of finitary Chevalley groups
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 2
\pages 133--142
\mathnet{http://mi.mathnet.ru/timm230}
\elib{https://elibrary.ru/item.asp?id=12878776}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 267
\issue , suppl. 1
\pages S118--S127
\crossref{https://doi.org/10.1134/S0081543809070128}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000274041900012}
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  • https://www.mathnet.ru/eng/timm/v15/i2/p133
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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