Group algebras with almost maximal lie nilpotency index

LetK G be a non-commutative Lie nilpotent group algebra of a groupG over a fieldK. It is known that the Lie nilpotency index ofKG is at most |G′|+1, where |G′| is the order of the commutator subgroup ofG. In 4] the groupsG for which this index is maximal were determined. Here we list theG’s for which it assumes the next highest possible value. The present paper is a part of the PhD dissertation of the author.