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Algebra Logika, 2019, Volume 58, Number 3, Pages 376–396 (Mi al902)  

This article is cited in 2 scientific papers (total in 2 papers)

Groups with finite Engel element

A. I. Sozutov

Siberian Federal University, Krasnoyarsk

Abstract: We prove that in an arbitrary group, the normal closure of a finite Engel element with Artinian centralizer is a locally nilpotent Cěrnikov subgroup, thereby generalizing the Baer–Suzuki theorem, Blackburn's and Shunkov's theorems.

Keywords: Engel element, finite element, locally nilpotent radical, Artinian group, Cěrnikov group, $D$-subgroup.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00566_a
A. I. Sozutov Supported by RFBR, project no. 19-01-00566-a.


DOI: https://doi.org/10.33048/alglog.2019.58.307

Full text: PDF file (274 kB)
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English version:
Algebra and Logic, 2019, 58:3, 254–267

Bibliographic databases:

UDC: 512.544
Received: 21.05.2018
Revised: 24.09.2019

Citation: A. I. Sozutov, “Groups with finite Engel element”, Algebra Logika, 58:3 (2019), 376–396; Algebra and Logic, 58:3 (2019), 254–267

Citation in format AMSBIB
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\by A.~I.~Sozutov
\paper Groups with finite Engel element
\jour Algebra Logika
\yr 2019
\vol 58
\issue 3
\pages 376--396
\mathnet{http://mi.mathnet.ru/al902}
\crossref{https://doi.org/10.33048/alglog.2019.58.307}
\transl
\jour Algebra and Logic
\yr 2019
\vol 58
\issue 3
\pages 254--267
\crossref{https://doi.org/10.1007/s10469-019-09544-0}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074812521}


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

    This publication is cited in the following articles:
    1. N. V. Maslova, I. N. Belousov, N. A. Minigulov, “Otkrytye problemy, sformulirovannye na XII shkole-konferentsii po teorii grupp, posvyaschennoi 85-letiyu V.A. Belonogova”, Tr. IMM UrO RAN, 26, no. 3, 2020, 275–285  mathnet  crossref  elib
    2. A. I. Sozutov, “Groups Saturated with Finite Frobenius Groups”, Math. Notes, 109:2 (2021), 270–279  mathnet  crossref  crossref  mathscinet  isi  elib
  • Алгебра и логика Algebra and Logic
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