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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 2group G containing a left 3Engel 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 language  English 

Pages (fromto)  48694882 
Number of pages  14 
Journal  Communications in Algebra 
Volume  49 
Issue number  11 
Early online date  5 Jun 2021 
DOIs  
Publication status  Published  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.
Keywords
 Engel elements
 Lie algebras
 locally finite groups
ASJC Scopus subject areas
 Algebra and Number Theory
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 1 Finished

Left 3Engel Elements in Groups
Engineering and Physical Sciences Research Council
1/08/17 → 31/05/22
Project: Research council