V. N. Knyagina, V. S. Monakhov, “On the permutability of $n$-maximal subgroups with Schmidt subgroups”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 125

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 3, Pages 125–130 (Mi timm846)

This article is cited in 12 scientific papers (total in 12 papers)

On the permutability of

$n$ -maximal subgroups with Schmidt subgroups

V. N. Knyagina^a, V. S. Monakhov^b

^a Gomel Engineering Institute, Ministry of Extraordinary Situations of the Republic of Belarus
^b Francisk Skorina Gomel State University

Full-text PDF (148 kB) Citations (12)

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Abstract: A Schmidt group is a nonnilpotent group in which every proper subgroup is nilpotent. Let us fix a positive integer

$n$ and assume that each

$n$ -maximal subgroup of a finite group

$G$ is permutable with any Schmidt subgroup. We prove that, if

$n\in\{1,2,3\}$ , then

$G$ is metanilpotent and, if

$n\ge4$ and

$G$ is solvable, then the nilpotent length of

$G$ is at most

$n-1$ .

Keywords: finite group, solvable group, Schmidt subgroup, nilpotent length.

Received: 21.11.2011

Bibliographic databases:

Document Type: Article

UDC: 512.542

Language: Russian

Citation: V. N. Knyagina, V. S. Monakhov, “On the permutability of

$n$ -maximal subgroups with Schmidt subgroups”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 125–130

Citation in format AMSBIB

\Bibitem{KnyMon12}

\by V.~N.~Knyagina, V.~S.~Monakhov

\paper On the permutability of $n$-maximal subgroups with Schmidt subgroups

\serial Trudy Inst. Mat. i Mekh. UrO RAN

\yr 2012

\vol 18

\issue 3

\pages 125--130

\mathnet{http://mi.mathnet.ru/timm846}

\elib{https://elibrary.ru/item.asp?id=17937017}

Linking options:

https://www.mathnet.ru/eng/timm846

https://www.mathnet.ru/eng/timm/v18/i3/p125

This publication is cited in the following 12 articles:

E. V. Zubei, “Konechnye gruppy s $OS$-properestanovochnymi podgruppami”, Chebyshevskii sb., 22:3 (2021), 457–463
V. I. Murashka, “Groups with prescribed systems of Schmidt subgroups”, Siberian Math. J., 60:2 (2019), 334–342
Guo W., Skiba A.N., “Finite Groups Whose N-Maximal Subgroups Are SIGMA-Subnormal”, Sci. China-Math., 62:7 (2019), 1355–1372
E. V. Zubei, “O perestanovochnosti silovskikh podgrupp s kommutantami B-podgrupp”, Zhurn. Belorus. gos. un-ta. Matem. Inf., 1 (2019), 12–17
B. Hu, J. Huang, A. N. Skiba, “On generalized $S$-quasinormal and generalized subnormal subgroups of finite groups”, Commun. Algebr., 46:4 (2018), 1758–1769
J. Huang, B. Hu, X. Zheng, “Finite groups whose $n$-maximal subgroups are modular”, Siberian Math. J., 59:3 (2018), 556–564
Hu B., Huang J., “On Generalized Modular Subgroups of Finite Groups”, Bull. Iran Math. Soc., 44:6 (2018), 1415–1426
Bin Hu, Jianhong Huang, A. N. Skiba, “Finite groups whose $n$-maximal subgroups are generalized $S$-quasinormal”, PFMT, 2017, no. 2(31), 40–45
A. N. Skiba, “On $\sigma$-properties of finite groups III”, PFMT, 2016, no. 1(26), 52–62
V. A. Kovaleva, “Konechnye gruppy s zadannymi obobschenno maksimalnymi podgruppami (obzor). I. Konechnye gruppy s obobschenno normalnymi $n$-maksimalnymi podgruppami”, PFMT, 2016, no. 4(29), 48–58
V. N. Knyagina, “O perestanovochnosti $n$-maksimalnykh podgrupp c $p$-nilpotentnymi podgruppami Shmidta”, Tr. In-ta matem., 24:1 (2016), 34–37
V. A. Kovaleva, Xiaolan Yi, “Finite groups with all $n$-maximal ($n = 2, 3$) subgroups $K$-$\mathfrak{U}$-subnormal”, PFMT, 2014, no. 2(19), 59–63

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

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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