2005/07/13 by Victor Bovdi, Bovdi, Victor, Tibor Juhasz +4
Mathematics · #16S34 #17B30 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #math.RA #msc:16S34 #msc:17B30
paper · pdf · doi:10.48550/arxiv.math/0507261
arxiv created 2005/07/13 · openalex publication_date 2005/07/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be a field of positive characteristic p and KG the group algebra of a group G. It is known that, if KG is Lie nilpotent, then its upper (or lower) Lie nilpotency index is at most |G'|+1, where |G'| is the order of the commutator subgroup. The authors have previously determined the groups G for which this index is maximal and here they determine the G for which it is `almost maximal', that is the next highest possible value, namely |G'|-p+2.