W. Guo, N. V. Maslova, D. O. Revin, “On the pronormality of subgroups of odd index in some extensions of finite groups”, Sibirsk. Mat. Zh., 59:4 (2018), 773–790; Siberian Math. J., 59:4 (2018), 610

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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 4, Pages 773–790
DOI: https://doi.org/10.17377/smzh.2018.59.404 (Mi smj3009)

This article is cited in 10 scientific papers (total in 10 papers)

On the pronormality of subgroups of odd index in some extensions of finite groups

W. Guo^a, N. V. Maslova^bc, D. O. Revin^dea

^a University of Science and Technology of China, Hefei, P. R. China
^b Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russia
^c Ural Federal University, Ekaterinburg, Russia
^d Sobolev Institute of Mathematics, Novosibirsk, Russia
^e Novosibirsk State University, Novosibirsk, Russia

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DOI: https://doi.org/10.17377/smzh.2018.59.404

Abstract: We study finite groups with the following property

(*)

$(*)$ : All subgroups of odd index are pronormal. Suppose that

G

$G$ has a normal subgroup

A

$A$ with property

(*)

$(*)$ , and the Sylow

2

$2$ -subgroups of

G / A

$G/A$ are self-normalizing. We prove that

G

$G$ has property

(*)

$(*)$ if and only if so does

N_{G} (T) / T

$N_G(T)/T$ , where

T

$T$ is a Sylow

2

$2$ -subgroup of

A

$A$ . This leads to a few results that can be used for the classification of finite simple groups with property

(*)

$(*)$ .

Keywords: finite group, pronormal subgroup, Sylow

2

$2$ -subgroup, subgroup of odd index, wreath product, direct product, self-normalizing subgroup, simple group, symplectic group.

Funding agency	Grant number
National Natural Science Foundation of China	11771409
Ministry of Education and Science of the Russian Federation	МК-6118.2016.1 02.A03.21.0006
CAS President's International Fellowship Initiative	2016VMA078
Russian Academy of Sciences - Federal Agency for Scientific Organizations	I.1.1, 0314-2016-0001
The first author was supported by the NNSF of China (Grant 11771409). The second author was supported by the President of the Russian Federation (Grant MK-6118.2016.1) and the State Maintenance Program for the Leading Universities of the Russian Federation (Agreement 02.A03.21.0006 of 27.08.2013). The third author was supported by the CAS President's International Fellowship Initiative (Grant 2016VMA078) and the Program of Fundamental Scientific Research of the Siberian Branch of the Russian Academy of Sciences No. I.1.1 (Project 0314- 2016-0001).

Received: 11.10.2017

English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 4, Pages 610–622
DOI: https://doi.org/10.1134/S0037446618040043

Bibliographic databases:

Document Type: Article

UDC: 512.542

Language: Russian

Citation: W. Guo, N. V. Maslova, D. O. Revin, “On the pronormality of subgroups of odd index in some extensions of finite groups”, Sibirsk. Mat. Zh., 59:4 (2018), 773–790; Siberian Math. J., 59:4 (2018), 610–622

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/smj3009

https://www.mathnet.ru/eng/smj/v59/i4/p773

This publication is cited in the following 10 articles:

W. Guo, N. V. Maslova, D. O. Revin, “Nonpronormal subgroups of odd index in finite simple linear and unitary groups”, Proc. Steklov Inst. Math. (Suppl.), 325, suppl. 1 (2024), S114–S122
Mingzhu Chen, Ilya Gorshkov, Natalia V. Maslova, Nanying Yang, “On combinatorial properties of Gruenberg–Kegel graphs of finite groups”, Monatsh Math, 2024
Mattia Brescia, Marco Trombetti, “Locally finite simple groups whose non-Abelian subgroups are pronormal”, Communications in Algebra, 51:8 (2023), 3346
N. V. Maslova, D. O. Revin, “On the pronormality of subgroups of odd index in some direct products of finite groups”, J. Algebra Appl., 22:04 (2023)
S. Liu, H. Yu, “A note on pronormal p-subgroups of finite groups”, Mon.heft. Math., 195:1 (2021), 173–176
Guo Wen Bin, A. S. Kondrat'ev, N. V. Maslova, L. Miao, “Finite Groups Whose Maximal Subgroups Are Solvable or Have Prime Power Indices”, Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S47–S51
A. S. Kondrat'ev, N. V. Maslova, D. O. Revin, “Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal”, J. Group Theory, 23:6 (2020), 999–1016
J. Liu, J. Chang, G. Chen, “Finite groups with some pronormal subgroups”, J. Algebra. Appl., 19:6 (2020), 2050110
Anatoly S. Kondrat'ev, Natalia Maslova, Danila Revin, Groups St Andrews 2017 in Birmingham, 2019, 406
Guo W., Revin D.O., “Pronormality and Submaximal (Sic)-Subgroups on Finite Groups”, Commun. Math. Stat., 6:3, SI (2018), 289–317

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

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