On Polynilpotent Multipliers of Free Nilpotent Groups

TL;DR

This paper explicitly describes the structure of the Baer invariant for free nilpotent groups within certain polynilpotent varieties, extending understanding of their algebraic properties and invariants.

Contribution

It provides an explicit structure for the Baer invariant of free nilpotent groups relative to polynilpotent varieties of class row (c,1), for all c > 2n-2.

Findings

Explicit structure of Baer invariant for free nilpotent groups.

Structure of Baer invariant for free abelian groups in metabelian variety.

Applicable to all c > 2n-2 in the specified variety.

Abstract

In this paper, we present an explicit structure for the Baer invariant of a free nilpotent group (the $n$-th nilpotent product of the infinite cyclic group, $\textbf{Z}\st{n}* \textbf{Z}\st{n}*... \st{n}*\textbf{Z}$) with respect to the variety of polynilpotent groups of class row $(c,1)$, ${\cal N}_{c,1}$, 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.