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Uspekhi Mat. Nauk, 2011, Volume 66, Issue 5(401), Pages 3–46 (Mi umn9440)  

This article is cited in 33 scientific papers (total in 33 papers)

Theorems of Sylow type

E. P. Vdovinab, D. O. Revinab

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

Abstract: Let $\pi$ be a set of primes. Generalizing the known properties of Sylow subgroups, Hall introduced the classes $E_\pi$, $C_\pi$, and $D_\pi$ of finite groups that contain a Hall $\pi$-subgroup, precisely one conjugacy class of Hall $\pi$-subgroups, and precisely one conjugacy class of maximal $\pi$-subgroups, respectively. The present paper concerns results about $E_\pi$, $C_\pi$, and $D_\pi$ that have been obtained by different authors at different times.
Bibliography: 113 titles.

Keywords: Hall subgroup, finite group, finite simple group, Hall property, existence criterion for Hall subgroups, conjugacy criterion for Hall subgroups, finite groups of Lie type, an analogue of Sylow's theorem for Hall subgroups.

DOI: https://doi.org/10.4213/rm9440

Full text: PDF file (1055 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2011, 66:5, 829–870

Bibliographic databases:

UDC: 512.542
MSC: Primary 20D20; Secondary 20D06, 20D08, 20D10
Received: 07.10.2010

Citation: E. P. Vdovin, D. O. Revin, “Theorems of Sylow type”, Uspekhi Mat. Nauk, 66:5(401) (2011), 3–46; Russian Math. Surveys, 66:5 (2011), 829–870

Citation in format AMSBIB
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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. Bashun S.Yu., “Finite Simple Groups With Hall (2, R)-Subgroups, R (G)\(2, T), T (G)”, Ukr. Math. J.  crossref  isi
    2. Buturlakin A.A., Khramova A.P., “a Criterion For the Existence of a Solvable Pi-Hall Subgroup in a Finite Group”, Commun. Algebr.  crossref  isi
    3. N. Ch. Manzaeva, “Reshenie problemy Vilanda dlya sporadicheskikh grupp”, Sib. elektron. matem. izv., 9 (2012), 294–305  mathnet
    4. E. P. Vdovin, D. O. Revin, “Pronormality of Hall subgroups in finite simple groups”, Siberian Math. J., 53:3 (2012), 419–430  mathnet  crossref  mathscinet  isi
    5. Maslova N.V., Revin D.O., “Svoistva konechnykh grupp s khollovymi maksimalnymi podgruppami”, Matematicheskii forum (Itogi nauki. Yug Rossii), 6 (2012), 113–121  elib
    6. Revin D.O., “O svoistve $\mathcal C_\pi$ v reshetke nadgrupp $\pi$-khollovoi podgruppy”, Matematicheskii forum (Itogi nauki. Yug Rossii), 6 (2012), 146–151  elib
    7. A. Moretó, “Sylow numbers and nilpotent Hall subgroups”, J. Algebra, 379 (2013), 80–84  crossref  mathscinet  zmath  isi
    8. E. P. Vdovin, D. O. Revin, “On the pronormality of Hall subgroups”, Siberian Math. J., 54:1 (2013), 22–28  mathnet  crossref  mathscinet  isi
    9. E. P. Vdovin, D. O. Revin, “Pronormality and strong pronormality of subgroups”, Algebra and Logic, 52:1 (2013), 15–23  mathnet  crossref  mathscinet  zmath  isi
    10. E. M. Palchik, “O konechnykh faktorizuemykh gruppakh”, Tr. IMM UrO RAN, 19, no. 3, 2013, 261–267  mathnet  mathscinet  elib
    11. E. P. Vdovin, D. O. Revin, “Neradikalnost klassa $E_\pi$-grupp”, Tr. In-ta matem., 21:1 (2013), 35–39  mathnet
    12. E. P. Vdovin, “On intersection of solvable Hall subgroups in finite simple exceptional groups of Lie type”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S183–S190  mathnet  crossref  mathscinet  isi  elib
    13. N. Ch. Manzaeva, “Heritability of the property $\mathcal D_\pi$ by overgroups of $\pi$-Hall subgroups in the case where $2\in\pi$”, Algebra and Logic, 53:1 (2014), 17–28  mathnet  crossref  mathscinet  isi
    14. D. O. Revin, E. P Vdovin, “Frattini argument for Hall subgroups”, J. Algebra, 414 (2014), 95–104  crossref  mathscinet  zmath  isi  elib
    15. E. M. Palchik, “Konechnye prostye gruppy s faktorizatsiei $G=G_\pi B$, $2\notin\pi$”, Tr. IMM UrO RAN, 20, no. 2, 2014, 242–249  mathnet  mathscinet  elib
    16. W. Guo, D. O. Revin, “On the class of groups with pronormal Hall $\pi$-subgroups”, Siberian Math. J., 55:3 (2014), 415–427  mathnet  crossref  mathscinet  isi  elib  elib
    17. 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
    18. E. M. Pal'chik, “On the finite groups whose Sylow $3$-subgroup normalizes a Sylow $3'$-subgroup”, Siberian Math. J., 56:1 (2015), 132–137  mathnet  crossref  mathscinet  isi  elib  elib
    19. Wenbin Guo, D.O. Revin, E.P. Vdovin, “Confirmation for Wielandt's conjecture”, J. Algebra, 434 (2015), 193–206  crossref  mathscinet  zmath  isi
    20. E. P. Vdovin, D. O. Revin, “The existence of pronormal $\pi$-Hall subgroups in $E_\pi$-groups”, Siberian Math. J., 56:3 (2015), 379–383  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    21. A. Kh. Zhurtov, Z. B. Selyaeva, “O lokalno konechnykh $\pi$-razdelimykh gruppakh”, Vladikavk. matem. zhurn., 17:2 (2015), 16–21  mathnet
    22. A. A. Heliel, A. Ballester-Bolinches, R. Esteban-Romero, M. O. Almestady, “$\mathfrak Z$-permutable subgroups of finite groups”, Monatsh. Math., 2016  crossref  mathscinet
    23. N. V. Maslova, D. O. Revin, “Nonabelian composition factors of a finite group whose maximal subgroups of odd indices are Hall subgroups”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 148–157  mathnet  crossref  crossref  mathscinet  isi  elib
    24. E. P. Vdovin, D. O. Revin, “Abnormality criteria for $p$-complements”, Algebra and Logic, 55:5 (2016), 347–353  mathnet  crossref  crossref  isi
    25. E. P. Vdovin, M. N. Nesterov, D. O. Revin, “Pronormality of Hall subgroups in their normal closure”, Algebra and Logic, 56:6 (2018), 451–457  mathnet  crossref  crossref  isi
    26. M. N. Nesterov, “On pronormality and strong pronormality of Hall subgroups”, Siberian Math. J., 58:1 (2017), 128–133  mathnet  crossref  crossref  isi  elib  elib
    27. Guo W., Revin D.O., “Classification and Properties of the -Submaximal Subgroups in Minimal Nonsolvable Groups”, Bull. Math. Sci., 8:2 (2018), 325–351  crossref  mathscinet  zmath  isi  scopus
    28. W. Guo, D. O. Revin, “Maximal and submaximal $\mathfrak X$-subgroups”, Algebra and Logic, 57:1 (2018), 9–28  mathnet  crossref  crossref  isi
    29. Guo Wen Bin, A. A. Buturlakin, D. O. Revin, “Equivalence of the existence of nonconjugate and nonisomorphic Hall $\pi$-subgroups”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 94–99  mathnet  crossref  crossref  isi  elib
    30. W. Guo, D. O. Revin, “Conjugacy of maximal and submaximal $\mathfrak X$-subgroups”, Algebra and Logic, 57:3 (2018), 169–181  mathnet  crossref  crossref  isi
    31. Guo W., Revin D.O., “Pronormality and Submaximal (Sic)-Subgroups on Finite Groups”, Commun. Math. Stat., 6:3, SI (2018), 289–317  crossref  mathscinet  isi  scopus
    32. Zhang J., Miao L., Bao H., “On Nearly -Supplemented Primary Subgroups of Finite Groups”, Commun. Algebr., 47:2 (2019), 896–903  crossref  mathscinet  zmath  isi  scopus
    33. E. P. Vdovin, N. Ch. Manzaeva, D. O. Revin, “On the heritability of the Sylow $\pi$-theorem by subgroups”, Sb. Math., 211:3 (2020), 309–335  mathnet  crossref  crossref  isi
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