Left 3-Engel elements in locally finite 2-groups

Anastasia Hadjievangelou, Gunnar Traustason

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)


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
Issue number11
Early online date5 Jun 2021
Publication statusPublished - 31 Dec 2021

Bibliographical note

Funding Information:
The first author is partially supported by ‘The Norton Scholarship’. We acknowledge the EPSRC (grant number 16523160) for support. Moreover, we would like to thank Marialaura Noce for drawing our attention to Lucas’ Theorem.


  • Engel elements
  • Lie algebras
  • locally finite groups

ASJC Scopus subject areas

  • Algebra and Number Theory


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