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Groups with Finite Engel Element

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Algebra and Logic Aims and scope

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

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Authors and Affiliations

  1. Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, 660041, Russia

    A. I. Sozutov

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  1. A. I. Sozutov
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Correspondence to A. I. Sozutov.

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A. I. Sozutov Supported by RFBR, project no. 19-01-00566-a.

Translated from Algebra i Logika, Vol. 58, No. 3, pp. 376-396,May-June, 2019.

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Sozutov, A.I. Groups with Finite Engel Element. Algebra Logic 58, 254–267 (2019). https://doi.org/10.1007/s10469-019-09544-0

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  • DOI: https://doi.org/10.1007/s10469-019-09544-0

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