Pregroups and hyperbolicity

TL;DR

This paper establishes specific axioms on pregroups that guarantee their universal groups are word-hyperbolic, advancing understanding of hyperbolic group structures.

Contribution

It introduces a set of axioms on pregroups that ensure their universal groups are hyperbolic, linking pregroup properties to hyperbolic group theory.

Findings

Identified axioms on pregroups that imply hyperbolicity of universal groups

Provided conditions under which a finitely generated group is hyperbolic

Enhanced the theoretical framework connecting pregroups and hyperbolic groups

Abstract

In this paper we study hyperbolicty of the universal group $U(P)$ of a pregroup $P$. Given a finitely generated group $G$ and a pregroup $P$ such that $G \simeq U(P)$, we provide a particular set of axioms on $P$ which ensure that $G$ is word-hyperbolic.