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Trudy Inst. Mat. i Mekh. 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

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. Kondratev'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

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 267, suppl. 1, S118–S127

Bibliographic databases:

UDC: 512.542
Received: 19.01.2009

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
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\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{http://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{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000274041900012}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. S. Suleimanova, “On conjugacy in a Chevalley group of large Abelian subgroups of the unipotent subgroup”, J. Math. Sci., 169:5 (2010), 696–704  mathnet  crossref  mathscinet  elib  elib
    2. G. S. Suleimanova, “Klassy sopryazhennykh v gruppe Shevalle tipa $F_4$ bolshikh abelevykh podgrupp unipotentnoi podgruppy”, Vladikavk. matem. zhurn., 13:2 (2011), 45–55  mathnet  elib
    3. Galina S. Suleimanova, “Sopryazhennost v konechnoi gruppe Shevalle tipa $E_8$ bolshikh abelevykh unipotentnykh podgrupp”, Zhurn. SFU. Ser. Matem. i fiz., 4:4 (2011), 536–540  mathnet
    4. V. M. Levchuk, G. S. Suleimanova, “The normal structure of the unipotent subgroup in Lie type groups and its extremal subgroups”, J. Math. Sci., 185:3 (2012), 448–457  mathnet  crossref
    5. Levchuk V.M., Suleimanova G.S., “Extremal and maximal normal abelian subgroups of a maximal unipotent subgroup in groups of Lie type”, J Algebra, 349:1 (2012), 98–116  crossref  mathscinet  zmath  isi  elib  scopus
    6. Vladimir M. Levchuk, Galina S. Suleimanova, “Thompson subgroups and large abelian unipotent subgroups of Lie-type groups”, Zhurn. SFU. Ser. Matem. i fiz., 6:1 (2013), 63–73  mathnet
    7. G. S. Suleimanova, “Bolshie elementarnye abelevy unipotentnye podgruppy grupp lieva tipa”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 6:2 (2013), 69–76  mathnet
    8. V. M. Levchuk, A. V. Litavrin, N. D. Khodyunya, V. V. Tsygankov, “Niltreugolnye podalgebry algebr Shevalle i ikh obobscheniya”, Vladikavk. matem. zhurn., 17:2 (2015), 37–46  mathnet
    9. Yu. V. Bekker, V. M. Levchuk, E. A. Sotnikova, “Nefinitarnye obobscheniya niltreugolnykh podalgebr algebr Shevalle”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 29 (2019), 39–51  mathnet  crossref
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