Left 3-Engel elements in locally finite 2-groups

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Abstract

We give an infinite family of examples that generalize the construction given by Noce, Tracey and Traustason of a locally finite 2-group G containing a left 3-Engel element x where (Formula presented.) the normal closure of x in G, is not nilpotent. The construction is based on a family of Lie algebras that are of interest in their own right and make use of a classical theorem of Lucas, regarding when (Formula presented.) is even.

Original languageEnglish
Pages (from-to)4869-4882
Number of pages14
JournalCommunications in Algebra
Volume49
Issue number11
Early online date5 Jun 2021
DOIs
Publication statusPublished - 31 Dec 2021

Keywords

  • Engel elements
  • Lie algebras
  • locally finite groups

ASJC Scopus subject areas

  • Algebra and Number Theory

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