New embeddings between the Higman-Thompson groups

TL;DR

This paper provides a direct proof showing that all Higman-Thompson groups of the form G_{k,1} are mutually embeddable, extending Higman's original embeddings and confirming recent results by Matte Bon.

Contribution

It offers a new, direct proof of the mutual embeddability of Higman-Thompson groups, extending classical results and simplifying the understanding of their structure.

Findings

All G_{k,1} groups embed into each other

Extension of Higman's original embeddings

Supports recent results by Matte Bon

Abstract

We give a direct proof that all Higman-Thompson groups of the form $G_{k,1}$ (for $k \ge 2$) are embedded in one another, which is a recent result of N. Matte Bon. This extends the embeddings given by Higman in 1974.