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Mat. Zametki, 1997, Volume 62, Issue 4, Pages 577–587 (Mi mz1640)  

This article is cited in 3 scientific papers (total in 3 papers)

Characterization of generalized Chernikov groups among groups with involutions

V. I. Senashov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: The class of generalized Chernikov groups is characterized, i.e., the class of periodic locally solvable groups with the primary ascending chain condition. The name of the class is related to the fact that the structure of such groups is close to that of Chernikov groups. Namely, a Chernikov group is defined as a finite extension of a direct product of finitely many quasi-cyclic groups, and a generalized Chernikov group is a layer-finite extension of a direct product $A$ of quasi-cyclic $p$-groups with finitely many factors for each prime $p$ such that each of its elements does not commute elementwise with only finitely many Sylow subgroups of $A$. A theorem that characterizes the generalized Chernikov groups in the class of groups with involution is proved.

DOI: https://doi.org/10.4213/mzm1640

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English version:
Mathematical Notes, 1997, 62:4, 480–487

Bibliographic databases:

UDC: 512.54
Received: 19.01.1995
Revised: 15.10.1996

Citation: V. I. Senashov, “Characterization of generalized Chernikov groups among groups with involutions”, Mat. Zametki, 62:4 (1997), 577–587; Math. Notes, 62:4 (1997), 480–487

Citation in format AMSBIB
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\pages 577--587
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\transl
\jour Math. Notes
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Senashov, “Characterization of groups with generalized Chernikov periodic part”, Math. Notes, 67:2 (2000), 218–222  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. I. Senashov, A. I. Sozutov, V. P. Shunkov, “Investigation of groups with finiteness conditions in Krasnoyarsk”, Russian Math. Surveys, 60:5 (2005), 805–848  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Vladimir I. Senashov, “Sharacterizations of Layer-Finite Groups and Their Extensions”, Zhurn. SFU. Ser. Matem. i fiz., 2:3 (2009), 279–287  mathnet  elib
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