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Algebra Logika, 2013, Volume 52, Number 1, Pages 22–33 (Mi al569)  

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

Pronormality and strong pronormality of subgroups

E. P. Vdovinab, D. O. Revinba

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

Abstract: A subgroup $H$ of a group $G$ is said to be pronormal if, for any element $g\in G$, subgroups $H$ and $H^g$ are conjugate in $\langle H,H^g\rangle$. A subgroup $H$ of a group $G$ is said to be strongly pronormal if, for any subgroup $K\le H$ and any element $g\in G$, there exists an element $x\in\langle H,K^g\rangle$ such that $K^{gx}\le H$. Many known examples of pronormal subgroups, namely, normal subgroups, maximal subgroups, Sylow subgroups of finite groups, and Hall subgroups of finite soluble groups, will also exemplify strongly pronormal subgroups. It is shown that Carter subgroups of finite groups (which are always pronormal) are not strongly pronormal in general, even in soluble groups.

Keywords: pronormal group, strongly pronormal group, Carter subgroup, finite group.

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English version:
Algebra and Logic, 2013, 52:1, 15–23

Bibliographic databases:

UDC: 512.542
Received: 01.08.2012

Citation: E. P. Vdovin, D. O. Revin, “Pronormality and strong pronormality of subgroups”, Algebra Logika, 52:1 (2013), 22–33; Algebra and Logic, 52:1 (2013), 15–23

Citation in format AMSBIB
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\paper Pronormality and strong pronormality of subgroups
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\vol 52
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\jour Algebra and Logic
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\pages 15--23
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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. 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. 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
  • Алгебра и логика Algebra and Logic
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