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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2018, Volume 24, Number 3, Pages 281–285
DOI: https://doi.org/10.21538/0134-4889-2018-24-3-281-285
(Mi timm1569)
 

This article is cited in 7 scientific papers (total in 7 papers)

On a periodic part of a Shunkov group saturated with wreathed groups

A. A. Shlepkin

Institute of Space and Information Technologies, Siberian Federal University
Full-text PDF (160 kB) Citations (7)
References:
Abstract: A group $G$ is saturated with groups from a set of groups $\mathfrak{X}$ if any finite subgroup $K$ of $G$ is contained in a subgroup of $G$ isomorphic to some group from $\mathfrak{X}$. A group $G$ is called a Shunkov group (a conjugately biprimitively finite group) if, for any finite subgroup $H$ of $G$, any two conjugate elements of prime order in the quotient group $N_G(H)/h$ generate a finite group. Let $G$ be a group. If all elements of finite orders from $G$ are contained in a periodic subgroup of $G$, then it is called a periodic part of $G$ and is denoted by $t(G)$. It is known that a Shunkov group may have no periodic part. The existence of a periodic part of a Shunkov group saturated with finite wreathed groups is proved and the structure of the periodic part is established.
Keywords: group saturated with a set of groups, Shunkov group.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00257
This work was supported by the Russian Foundation for Basic Research (project no. 18-31-00257).
Received: 05.06.2018
Bibliographic databases:
Document Type: Article
UDC: 512.54
MSC: 20K01
Language: Russian
Citation: A. A. Shlepkin, “On a periodic part of a Shunkov group saturated with wreathed groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 3, 2018, 281–285
Citation in format AMSBIB
\Bibitem{Shl18}
\by A.~A.~Shlepkin
\paper On a periodic part of a Shunkov group saturated with wreathed groups
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 3
\pages 281--285
\mathnet{http://mi.mathnet.ru/timm1569}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-3-281-285}
\elib{https://elibrary.ru/item.asp?id=35511294}
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  • https://www.mathnet.ru/eng/timm/v24/i3/p281
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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