Factors of the nilpotent series of certain metabelian groups of primary exponent

Abstract

By using an additive technique proposed earlier by the author, defining relations in the factors of the nilpotent series of the maximal metabelian 2-generated groups of exponent p2 are found. A comparison of the upper bound 2p2−3 thus obtained for the nilpotency class with the exact bound 2 (p2−p), obtained in the paper abstracted in RZMat, 1969, 3A180, shows that the list of relations obtained is not complete. Further, it is shown as to how, by increasing the precision of computations, one succeeds in achieving a definitive description of such groups for the exponents 9 and 8.