A NEW ALGORITHM FOR FINDING THE NILPOTENCY CLASS OF A FINITE p-GROUP DESCRIBING THE UPPER CENTRAL SERIES
نویسنده
چکیده
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 the algorithm always runs. The algorithm describes a sequence of ideals of the Jacobson radical, J , and because ∆(G) = J +1, this sequence induces the upper central series in ∆(G).
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