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Mathematics of the USSR-Sbornik, 1979, Volume 35, Issue 4, Pages 569–580
DOI: https://doi.org/10.1070/SM1979v035n04ABEH001573 (Mi sm2675) 		 
This article is cited in 3 scientific papers (total in 4 papers)

A characterization of infinite Chernikov groups that are not finite extensions of quasi-cyclic groups

A. A. Shafiro, V. P. Shunkov
English version PDF (1013 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM1979v035n04ABEH001573
Abstract: We characterize the groups named in the title. Our main result is as follows: an infinite locally finite group $G$ that is not a finite extension of a quasi-cyclic group is a Chernikov group if and only if it has a subgroup $H$ of finite index whose holomorph contains a copy of the four-group in such a way that the centralizer in $H$ of each of its three involutions is a Chernikov group.
Bibliography: 17 titles.
Received: 26.01.1977 and 18.01.1978
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1978, Volume 107(149), Number 2(10), Pages 289–303
Bibliographic databases:
UDC: 519.45
MSC: Primary 20E25; Secondary 20D05
Language: English
Original paper language: Russian
Citation: A. A. Shafiro, V. P. Shunkov, “A characterization of infinite Chernikov groups that are not finite extensions of quasi-cyclic groups”, Mat. Sb. (N.S.), 107(149):2(10) (1978), 289–303; Math. USSR-Sb., 35:4 (1979), 569–580
Citation in format AMSBIB
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\by A.~A.~Shafiro, V.~P.~Shunkov
\paper A~characterization of infinite Chernikov groups that are not finite extensions of quasi-cyclic groups
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 107(149)
\issue 2(10)
\pages 289--303
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=512013}
\zmath{https://zbmath.org/?q=an:0423.20041|0393.20026}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 4
\pages 569--580
\crossref{https://doi.org/10.1070/SM1979v035n04ABEH001573}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JJ04900009}
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  • https://doi.org/10.1070/SM1979v035n04ABEH001573
  • https://www.mathnet.ru/eng/sm/v149/i2/p289
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:343
    Russian version PDF:97
    English version PDF:17
    References:63
     
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