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. Previously we determined the groups G for which the upper/lower nilpotency index is maximal or the upper nilpotency index is ‘almost maximal’ (that is, ...

In this paper we describe an algorithm for finding the nilpotency class, and the upper central series of the maximal normal p-subgroup ∆(G) of the automorphism group, Aut(G) of a bounded (or finite) abelian p-group G. This is the first part of two papers devoted to compute the nilpotency class of ∆(G) using formulas, and algorithms that work in almost all groups. Here, we prove that for p ≥ 3 t...