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Algebra Logika, 2008, Volume 47, Number 1, Pages 3–30 (Mi al343)  

This article is cited in 4 scientific papers (total in 4 papers)

Normalizers of subsystem subgroups in finite groups of Lie type

E. P. Vdovina, A. A. Gal'tb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University

Abstract: Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers of those quasisimple groups are structured. The present paper is devoted to tackling this problem.

Keywords: finite simple group of Lie type, reductive subgroup of maximal rank, subsystem subgroup.

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English version:
Algebra and Logic, 2008, 47:1, 1–17

Bibliographic databases:

UDC: 512.542
Received: 15.03.2007
Revised: 28.10.2007

Citation: E. P. Vdovin, A. A. Gal't, “Normalizers of subsystem subgroups in finite groups of Lie type”, Algebra Logika, 47:1 (2008), 3–30; Algebra and Logic, 47:1 (2008), 1–17

Citation in format AMSBIB
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    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. E. P. Vdovin, “Carter subgroups of finite groups”, Siberian Adv. Math., 19:1 (2009), 24–74  mathnet  crossref  mathscinet  elib  elib
    2. E. P. Vdovin, A. A. Gal't, “Strong reality of finite simple groups”, Siberian Math. J., 51:4 (2010), 610–615  mathnet  crossref  mathscinet  isi
    3. Revin D.O., Vdovin E.P., “On the number of classes of conjugate Hall subgroups in finite simple groups”, J. Algebra, 324:12 (2010), 3614–3652  crossref  mathscinet  zmath  isi  elib  scopus
    4. N. A. Vavilov, A. V. Shchegolev, “Overgroups of subsystem subgroups in exceptional groups: levels”, J. Math. Sci. (N. Y.), 192:2 (2013), 164–195  mathnet  crossref  mathscinet
  • Алгебра и логика Algebra and Logic
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