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Mat. Sb., 2012, Volume 203, Number 3, Pages 23–48 (Mi msb7803)  

This article is cited in 5 scientific papers (total in 5 papers)

Finite groups with Hall $\pi$-subgroups

V. A. Vedernikov

Moscow City Pedagogical University

Abstract: New classes of finite groups with Hall $\pi$-subgroups that have the Sylow properties are constructed and studied. The classes of groups $C_\pi$ and $D_\pi$ introduced by P. Hall are substantially extended. Necessary and sufficient conditions are established under which a finite group has Hall $\pi$-subgroups. $D$-Theorems generalizing $D$-theorems of P. Hall, Wielandt, Baer, and Hartley are obtained.
Bibliography: 30 titles.

Keywords: finite group, Hall $\pi$-subgroup, class of groups, formation.

DOI: https://doi.org/10.4213/sm7803

Full text: PDF file (649 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:3, 326–350

Bibliographic databases:

UDC: 512.542
MSC: Primary 20D20; Secondary 20D10
Received: 22.10.2010 and 23.08.2011

Citation: V. A. Vedernikov, “Finite groups with Hall $\pi$-subgroups”, Mat. Sb., 203:3 (2012), 23–48; Sb. Math., 203:3 (2012), 326–350

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm7803
  • http://mi.mathnet.ru/eng/msb/v203/i3/p23

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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. V. A. Vedernikov, “Silovskie svoistva konechnykh grupp”, Tr. In-ta matem., 21:1 (2013), 40–47  mathnet
    2. E. P. Vdovin, “Groups of induced automorphisms and their application to studying the existence problem for Hall subgroups”, Algebra and Logic, 53:5 (2014), 418–421  mathnet  crossref  mathscinet  isi
    3. E. P. Vdovin, “The structure of groups possessing Carter subgroups of odd order”, Algebra and Logic, 54:2 (2015), 105–107  mathnet  crossref  crossref  mathscinet  isi
    4. V. A. Vedernikov, M. M. Sorokina, “The $\mathfrak F^\omega$-normalizers of finite groups”, Siberian Math. J., 58:1 (2017), 49–62  mathnet  crossref  crossref  isi  elib  elib
    5. Guo W., Vdovin E.P., “Number of Sylow Subgroups in Finite Groups”, J. Group Theory, 21:4 (2018), 695–712  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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