Correction: Root extraction in one-relator groups and slenderness

TL;DR

This paper corrects a previous argument regarding root extraction in one-relator groups and presents a related theorem, clarifying the theoretical understanding of group slenderness.

Contribution

It identifies and fixes a gap in earlier work and introduces a new theorem related to root extraction and slenderness in one-relator groups.

Findings

Correction of a previous proof gap

Introduction of a new related theorem

Enhanced understanding of group slenderness

Abstract

This very short correction notes a gap in an argument of an earlier paper, and also provides a theorem of similar flavor to the main result of that paper.