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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, Volume 30, Number 1, Pages 100–108
DOI: https://doi.org/10.21538/0134-4889-2024-30-1-100-108 (Mi timm2065) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Finite groups with $\mathbb{P}$-subnormal Schmidt subgroups

X. Yia, Zh. Xua, S. F. Kamornikovb

a Zhejiang Sci-tech University
b Gomel State University named after Francisk Skorina
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DOI: https://doi.org/10.21538/0134-4889-2024-30-1-100-108
Abstract: A subgroup $H$ of a group $G$ is called $\mathbb{P}$-subnormal in $G$ whenever either $H = G$ or there is a chain of subgroups
$$H = H_0 \subset H_1 \subset \ldots \subset H_n = G$$
such that $|H_i:H_{i-1}|$ is a prime for every $i = 1, 2,\ldots, n$. We study the structure of a finite group $G$ all of whose Schmidt subgroups are $\mathbb{P}$-subnormal. The obtained results complement the answer to Problem 18.30 in the Kourovka Notebook.
Keywords: finite group, $\mathbb{P}$-subnormal subgroup, Schmidt subgroup, saturated Fitting formation.
Funding agency Grant number
National Natural Science Foundation of China 12371021
Belarusian Republican Foundation for Fundamental Research Ф23РНФ-237
The research of the first author was supported by the National Natural Science Foundation of China (grant no. 12371021). The research of the third author was supported by the Belarusian Republican Foundation for Fundamental Research (project no. $\Phi$23PH$\Phi$-237).
Received: 05.12.2023
Revised: 08.01.2024
Accepted: 15.01.2024
English version:
Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2024, Volume 325, Issue 1, Pages S231–S238
DOI: https://doi.org/10.1134/S0081543824030179
Bibliographic databases:
Document Type: Article
UDC: 512.542
MSC: 20D20, 20D35
Language: Russian
Citation: X. Yi, Zh. Xu, S. F. Kamornikov, “Finite groups with $\mathbb{P}$-subnormal Schmidt subgroups”, Trudy Inst. Mat. i Mekh. UrO RAN, 30, no. 1, 2024, 100–108; Proc. Steklov Inst. Math., 325, suppl. 1 (2024), S231–S238
Citation in format AMSBIB
\Bibitem{YiXuKam24}
\by X.~Yi, Zh.~Xu, S.~F.~Kamornikov
\paper Finite groups with $\mathbb{P}$-subnormal Schmidt subgroups
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2024
\vol 30
\issue 1
\pages 100--108
\mathnet{http://mi.mathnet.ru/timm2065}
\crossref{https://doi.org/10.21538/0134-4889-2024-30-1-100-108}
\elib{https://elibrary.ru/item.asp?id=61885722}
\edn{https://elibrary.ru/phdtvi}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 325
\issue , suppl. 1
\pages S231--S238
\crossref{https://doi.org/10.1134/S0081543824030179}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85201691187}
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