  In this paper we describe an algorithm for finding the nilpotency class, and
the upper central series of the maximal normal p-subgroup N(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 N(G)
using formulas, and algorithms that work in almost all groups. Here, we prove
that for p>2 the algorithm always runs. The algorithm describes a sequence of
ideals of the Jacobson radical, J, and because N(G)=J+1, this sequence induces
the upper central series in N(G).
