2024/10/15 by Michael Vaughan-Lee, Vaughan-Lee, Michael
Mathematics · #17B30 #20D15 #20F45 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2410.11524
openalex publication_date 2024/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In my article 5-Engel algebras published on the arXiv in 2023 I proved that 5-Engel Lie algebras of characteristic zero or prime characteristic p>7 are nilpotent of class at most 11. In this note I investigate the ideal ID(x) generated by an element x in a 5-Engel Lie algebra. In characteristic 2 and 3 this ideal does not have to be nilpotent. For all primes p>3 I show that Id(x) is nilpotent in 5-Engel Lie algebras of characteristic p, and I obtain explicit (best possible) bounds on the nilpotency class.