Some Baer Invariants of Free Nilpotent Groups

TL;DR

This paper provides explicit structures and formulas for Baer invariants and polynilpotent multipliers of free nilpotent groups, advancing understanding of their algebraic properties within specific varieties and class conditions.

Contribution

It introduces explicit formulas for Baer invariants and polynilpotent multipliers of free nilpotent groups under new conditions, extending previous algebraic characterizations.

Findings

Explicit structure for Baer invariants of free nilpotent groups.

Formulas for polynilpotent multipliers for various class rows.

Results applicable to groups with specific nilpotency and variety conditions.

Abstract

We present an explicit structure for the Baer invariant of a free $n$th nilpotent group (the $n$th nilpotent product of infinite cyclic groups, $\textbf{Z}\st{n}* \textbf{Z}\st{n}*...\st{n}*\textbf{Z}$) with respect to the variety ${\cal V}$ with the set of words $V=\{[\ga_{c_1+1},\ga_{c_2+1}]\}$, for all $c_1\geq c_2$ and $2c_2-c_1>2n-2$. Also, an explicit formula for the polynilpotent multiplier of a free $n$th nilpotent group is given for any class row $(c_1,c_2,...,c_t)$, where $c_1\geq n$.