Lie Nilpotency Indices of Modular Group Algebras

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 tipper (or lower) Lie nilpotency index is at most vertical bar G'vertical bar +1, where vertical bar G'vertical bar is the order of the commutator subgroup. The class of groups G for which these indices are maximal or almost maximal has already been determined. Here we determine G for which tipper (or lower) Lie nilpotency index is the next highest possible.