Polynilpotent Multipliers of Finitely Generated Abelian Groups

TL;DR

This paper derives explicit formulas for the Baer invariant of finitely generated abelian groups within the framework of polynilpotent and solvable group varieties, enhancing understanding of their structural properties.

Contribution

It provides a new explicit formula for the Baer invariant of finitely generated abelian groups relative to polynilpotent and solvable group varieties.

Findings

Explicit structure of Baer invariants for polynilpotent groups

Formulas for $ ext{l}$-solvable multipliers of finitely generated abelian groups

Enhanced understanding of group invariants in algebraic structures

Abstract

In this paper, we present an explicit formula for the Baer invariant of a finitely generated abelian group with respect to the variety of polynilpotent groups of class row $(c_1,...,c_t)$, ${\cal N}_{c_1,...,c_t}$. In particular, one can obtain an explicit structure of the $\ell$-solvable multiplier (the Baer invariant with respect to the vaiety of solvable groups of length at most $\ell\geq 1,\ {\cal S}_{\ell}$.) of a finitely generated abelian group.