Monoids that map onto the Thompson-Higman groups

TL;DR

This paper introduces inverse monoids derived from Thompson-Higman groups that are finitely generated, residually finite, and closely related to their suffix expansions, offering new algebraic structures with interesting properties.

Contribution

It presents a novel modification of Thompson-Higman groups leading to inverse monoids with specific algebraic properties and connections to suffix expansions.

Findings

Inverse monoids map onto Thompson-Higman groups G_k1 and F_k1.

The inverse monoids are finitely generated and residually finite.

They are closely related to the suffix expansion of the groups.

Abstract

A slight modification of the definition of the Thompson-Higman groups G_k1 and F_k1 leads to inverse monoids that map onto G_k1 (respectively F_k1), and that have interesting properties: they are finitely generated, and residually finite. These inverse monoids are closely related to the suffix expansion of G_k1 (respectively F_k1).