Lie Dimension Subgroups and Central Series Related to Group Algebras

Abstract

Let KG be the group algebra of a group G over a field K of positive characteristic p, and let 𝔇(n)(G) and 𝔇[n](G) denote the n-th upper Lie dimension subgroup and the n-th lower one, respectively. In [1] and [12], the equality 𝔇(n)(G) =𝔇[n](G) is verified when p ≥ 5. Motivated by [16, Problem 55], in the present paper we establish it for particular classes of groups when p ≤ 3. Finally, we introduce and study a new central series of G linked with the Lie nilpotency class of KG.