Left 3-Engel elements in locally finite 2-groups

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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 ⟨x⟩G, 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 (mn) is even.
Original languageEnglish
JournalCommunications in Algebra
Early online date5 Jun 2021
Publication statusE-pub ahead of print - 5 Jun 2021

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