Presentations with negative deficiency and largeness

TL;DR

This paper extends previous work on balanced presentations by establishing conditions where groups with negative deficiency are large, contributing to the understanding of group largeness in algebraic topology.

Contribution

It provides new conditions under which presentations with negative deficiency can define large groups, expanding the theory of group presentations.

Findings

Identifies conditions for negative deficiency presentations to be large

Extends Edjvet's results on balanced presentations

Contributes to algebraic topology and group theory understanding

Abstract

We extend the results of M. Edjvet on balanced presentations and largeness by giving conditions under which presentations with negative deficiency define large groups.