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Algebra Logika, 2014, Volume 53, Number 1, Pages 26–44 (Mi al622)  

This article is cited in 2 scientific papers (total in 2 papers)

Heritability of the property $\mathcal D_\pi$ by overgroups of $\pi$-Hall subgroups in the case where $2\in\pi$

N. Ch. Manzaeva

Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: Let $\pi$ be a set of prime numbers. We say that a finite group $G$ is a $\mathcal D_\pi$-group if all of its maximal $\pi$-subgroups are conjugate. Question 17.44(b) in Unsolved Problems in Group Theory, The Kourovka Notebook, asks whether an overgroup of a $\pi$-Hall subgroup of a $\mathcal D_\pi$-group is always a $\mathcal D_\pi$-group. We give an affirmative answer to this question in the case where $2\in\pi$.

Keywords: finite group, $\pi$-Hall subgroup, $\mathcal D_\pi$-group, group of Lie type, finite simple group, maximal subgroup of odd index.

Full text: PDF file (218 kB)
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English version:
Algebra and Logic, 2014, 53:1, 17–28

Bibliographic databases:

UDC: 512.542
Received: 07.09.2013
Revised: 24.12.2013

Citation: N. Ch. Manzaeva, “Heritability of the property $\mathcal D_\pi$ by overgroups of $\pi$-Hall subgroups in the case where $2\in\pi$”, Algebra Logika, 53:1 (2014), 26–44; Algebra and Logic, 53:1 (2014), 17–28

Citation in format AMSBIB
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\by N.~Ch.~Manzaeva
\paper Heritability of the property $\mathcal D_\pi$ by overgroups of $\pi$-Hall subgroups in the case where~$2\in\pi$
\jour Algebra Logika
\yr 2014
\vol 53
\issue 1
\pages 26--44
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3237621}
\transl
\jour Algebra and Logic
\yr 2014
\vol 53
\issue 1
\pages 17--28
\crossref{https://doi.org/10.1007/s10469-014-9268-7}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902315824}


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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. 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
    2. 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  mathscinet  isi  elib
  • Алгебра и логика Algebra and Logic
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