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Sibirsk. Mat. Zh., 2012, Volume 53, Number 3, Pages 527–542 (Mi smj2343)  

This article is cited in 18 scientific papers (total in 18 papers)

Pronormality of Hall subgroups in finite simple groups

E. P. Vdovinab, D. O. Revinab

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

Abstract: We prove that the Hall subgroups of finite simple groups are pronormal. Thus we obtain an affirmative answer to Problem 17.45(a) of the Kourovka Notebook.

Keywords: Hall subgroup, pronormal subgroup, simple group.

Full text: PDF file (362 kB)
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English version:
Siberian Mathematical Journal, 2012, 53:3, 419–430

Bibliographic databases:

UDC: 512.542
Received: 28.06.2011

Citation: E. P. Vdovin, D. O. Revin, “Pronormality of Hall subgroups in finite simple groups”, Sibirsk. Mat. Zh., 53:3 (2012), 527–542; Siberian Math. J., 53:3 (2012), 419–430

Citation in format AMSBIB
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\paper Pronormality of Hall subgroups in finite simple groups
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\pages 527--542
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\vol 53
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\pages 419--430
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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. E. P. Vdovin, D. O. Revin, “On the pronormality of Hall subgroups”, Siberian Math. J., 54:1 (2013), 22–28  mathnet  crossref  mathscinet  isi
    2. 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
    3. 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
    4. Revin D.O., Vdovin E.P., “Frattini Argument For Hall Subgroups”, J. Algebra, 414 (2014), 95–104  crossref  mathscinet  zmath  isi  elib  scopus
    5. 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
    6. A. S. Kondrat'ev, N. V. Maslova, D. O. Revin, “On the pronormality of subgroups of odd index in finite simple groups”, Siberian Math. J., 56:6 (2015), 1101–1107  mathnet  crossref  crossref  mathscinet  isi  elib
    7. M. N. Nesterov, “Pronormalnost khollovykh podgrupp v pochti prostykh gruppakh”, Sib. elektron. matem. izv., 12 (2015), 1032–1038  mathnet  crossref
    8. A. S. Kondrat'ev, N. V. Maslova, D. O. Revin, “A pronormality criterion for supplements to abelian normal subgroups”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 145–150  mathnet  crossref  mathscinet  isi  elib
    9. E. P. Vdovin, D. O. Revin, “Abnormality criteria for $p$-complements”, Algebra and Logic, 55:5 (2016), 347–353  mathnet  crossref  crossref  isi
    10. 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
    11. A. S. Kondrat'ev, N. V. Maslova, D. O. Revin, “On the pronormality of subgroups of odd index in finite simple symplectic groups”, Siberian Math. J., 58:3 (2017), 467–475  mathnet  crossref  crossref  isi  elib  elib
    12. 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
    13. W. Guo, D. O. Revin, “Maximal and submaximal $\mathfrak X$-subgroups”, Algebra and Logic, 57:1 (2018), 9–28  mathnet  crossref  crossref  isi
    14. W. Guo, N. V. Maslova, D. O. Revin, “On the pronormality of subgroups of odd index in some extensions of finite groups”, Siberian Math. J., 59:4 (2018), 610–622  mathnet  crossref  crossref  isi  elib
    15. Go Ven Bin, A. A. Buturlakin, D. O. Revin, “Ekvivalentnost suschestvovaniya nesopryazhennykh i neizomorfnykh khollovykh $\pi$-podgrupp”, Tr. IMM UrO RAN, 24, no. 3, 2018, 43–50  mathnet  crossref  elib
    16. A. Kondratev, N. Maslova, D. Revin, “O pronormalnykh podgruppakh v konechnykh prostykh gruppakh”, Dokl. RAN, 482:1 (2018), 7–11  mathnet  crossref  mathscinet  zmath
    17. Guo W. Revin D.O., “Pronormality and Submaximal (Sic)-Subgroups on Finite Groups”, Commun. Math. Stat., 6:3, SI (2018), 289–317  crossref  mathscinet  zmath  isi  scopus
    18. 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
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