Left 3-Engel Elements in Locally Finite 2-Groups

2021/10/29 by Hadjievangelou, Anastasia, Traustason, Gunnar
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2110.15685

Abstract

We give an infinite family of examples that generalise the construction given in arXiv:1811.12074 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 \binommn is even.

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