Polynilpotent Capability of Finitely Generated Abelian Groups

TL;DR

This paper characterizes finitely generated abelian groups that are capable within the polynilpotent variety, extending Baer's classical result on capability.

Contribution

It generalizes Baer's capability classification to the broader context of polynilpotent varieties for finitely generated abelian groups.

Findings

Complete classification of polynilpotent capable finitely generated abelian groups.

Extension of capability results from abelian to polynilpotent varieties.

Significant generalization of classical capability theorems.

Abstract

In this paper we determine all finitely generated abelian groups which are varietal capable with respect to the variety of polynilpotent groups. This result is a vast generalization of the famous Baer's result about capability of finitely generated abelian groups.