On varieties of metabelian groups of prime-power exponent

Abstract

Let Un denote the variety of abelian groups of exponent dividing n, and let p be an arbitrary prime. In this paper all non-nilpotent, join-ireducible subvarieties of the product variety UpUp2 are determined. The proper subvarieties of this kind in fact form an infinite ascending chain …, and an arbitrary proper subvariety B of UpUp2 is either nilpotent or a join , where L is nilpotent and k is uniquely determined by B.