New embeddings between the Higman-Thompson groups

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.

Communicated by Karl Auinger

Keywords:

• Higman-Thompson groups
• combinatorial group theory
• group embeddings

MATHEMATICS SUBJECT CLASSIFICATION:

• 20E07
• 68R15
• 05E15

Acknowledgments

I would like to thank Matt Brin for many discussions. I’m grateful to Nicolás Matte Bon for contacting me after I posted the first version of this paper [4]. I would like to thank the referee for useful suggestions.