2024/11/01 by d'Elbée, Christian
#03C60 #17B30 #20F18 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2411.00669
We prove a version of the Wilson conjecture for ω-categorical 3-Engel Lie algebras over a field of characteristic 5: every ω-categorical Lie algebra over \mathbbF5 which satisfies the identity [x,y3] = 0 is nilpotent. We also include an extended introduction to Wilson's conjecture: every ω-categorical locally nilpotent p-group is nilpotent, and present variants of this conjecture and connections to local/global nilpotency problems (Burnside, Kurosh-Levitzki, Engel groups). No particular knowledge of model theory is assumed except basic notions of formulas and definable sets.