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Algebra and Logic

, Volume 58, Issue 3, pp 254–267 | Cite as

Groups with Finite Engel Element

  • A. I. SozutovEmail author
Article

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.

Keywords

Engel element finite element locally nilpotent radical Artinian group Cĕrnikov group D-subgroup 

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Siberian Federal UniversityKrasnoyarskRussia

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