W. Guo, D. O. Revin, “On the class of groups with pronormal Hall $\pi$-subgroups”, Sibirsk. Mat. Zh., 55:3 (2014), 509–524; Siberian Math. J., 55:3 (2014), 415

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Sibirskii Matematicheskii Zhurnal, 2014, Volume 55, Number 3, Pages 509–524 (Mi smj2549)

This article is cited in 6 scientific papers (total in 6 papers)

On the class of groups with pronormal Hall

$\pi$ -subgroups

W. Guo^a, D. O. Revin^bc

^a Department of Mathematics, University of Science and Technology of China, Hefei, P. R. China
^b Sobolev Institute of Mathematics, Novosibirsk, Russia
^c Novosibirsk State University, Novosibirsk, Russia

Full-text PDF (395 kB) Citations (6)

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Abstract: Given a set

$\pi$ of prime numbers, we define the class

$\mathscr P_\pi$ of all finite groups in which Hall

$\pi$ -subgroups exist and are pronormal by analogy with the Hall classes

$\mathscr E_\pi$ ,

$\mathscr C_\pi$ and

$\mathscr D_\pi$ . We study whether

$\mathscr P_\pi$ is closed under the main class-theoretic closure operations. In particular, we establish that

$\mathscr P_\pi$ is a saturated formation.

Keywords: finite group, Hall subgroup, pronormal subgroup, class of finite groups, properties

$\mathscr E_\pi$ ,

$\mathscr C_\pi$ and

$\mathscr D_\pi$ , property

$\mathscr P_\pi$ , class-theoretic closure operations, formation, saturated formation, Fitting class.

Received: 17.08.2013

English version:
Siberian Mathematical Journal, 2014, Volume 55, Issue 3, Pages 415–427
DOI: https://doi.org/10.1134/S0037446614030033

Bibliographic databases:

Document Type: Article

UDC: 512.542.6

Language: Russian

Citation: W. Guo, D. O. Revin, “On the class of groups with pronormal Hall

$\pi$ -subgroups”, Sibirsk. Mat. Zh., 55:3 (2014), 509–524; Siberian Math. J., 55:3 (2014), 415–427

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/smj2549

https://www.mathnet.ru/eng/smj/v55/i3/p509

This publication is cited in the following 6 articles:

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
W. Guo, D. O. Revin, “Pronormality and submaximal $\mathfrak{X}$ -subgroups on finite groups”, Commun. Math. Stat., 6:3, SI (2018), 289–317
W. Guo, D. O. Revin, “Classification and properties of the $\pi$ -submaximal subgroups in minimal nonsolvable groups”, Bull. Math. Sci., 8:2 (2018), 325–351
M. N. Nesterov, “On pronormality and strong pronormality of Hall subgroups”, Siberian Math. J., 58:1 (2017), 128–133
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	418
Full-text PDF :	120
References:	83
First page:	20

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