On Polynilpotent Multipliers of Free Nilpotent Groups

Abstract

In this article, we present an explicit structure for the Baer invariant of a free nilpotent group (the nth nilpotent product of the infinite cyclic group, ) with respect to the variety of polynilpotent groups of class row (c,1), 𝒩 c,1, for all c > 2n − 2. In particular, an explicit structure of the Baer invariant of a free Abelian group with respect to the variety of metabelian groups will be presented.