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Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 165–173 (Mi smj2849)  

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

On pronormality and strong pronormality of Hall subgroups

M. N. Nesterovab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We study several well-known questions on pronormality and strong pronormality of Hall subgroups. In particular, we exhibit the examples of finite groups (a) having a Hall subgroup not pronormal in its normal closure (this solves Problem 18.32 of The Kourovka Notebook in the negative); (b) having a Hall subgroup pronormal but not strongly pronormal; and (c) that are simple, having a Hall subgroup, and not strongly pronormal (this solves Problem 17.45(b) of The Kourovka Notebook in the negative).

Keywords: Hall subgroup, pronormal subgroup, strongly pronormal subgroup, finite simple group.

Funding Agency Grant Number
Russian Science Foundation 14-21-00065
The author was supported by the Russian Science Foundation (Grant 14-21-00065).


DOI: https://doi.org/10.17377/smzh.2017.58.116

Full text: PDF file (297 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:1, 128–133

Bibliographic databases:

UDC: 512.542
MSC: 35R30
Received: 03.03.2016

Citation: M. N. Nesterov, “On pronormality and strong pronormality of Hall subgroups”, Sibirsk. Mat. Zh., 58:1 (2017), 165–173; Siberian Math. J., 58:1 (2017), 128–133

Citation in format AMSBIB
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\paper On pronormality and strong pronormality of Hall subgroups
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\pages 165--173
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\pages 128--133
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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, 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
    2. 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
    3. W. Guo, D. O. Revin, “Pronormality and submaximal $\mathfrak{X}$-subgroups on finite groups”, Commun. Math. Stat., 6:3, SI (2018), 289–317  crossref  mathscinet  zmath  isi  scopus
    4. E. P. Vdovin, N. Ch. Manzaeva, D. O. Revin, “O nasleduemosti $\pi$-teoremy Silova podgruppami”, Matem. sb., 211:3 (2020), 3–31  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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