Work

The Higman--Thompson groups $V_n$ are $(2,2,2)$-generated

Year: 2024

Type: preprint

Abstract: We provide a family of generating sets $S_α$ of the Higman--Thompson groups $V_n$ that are parametrized by certain sequences $α$ of elements in $V_n$. These generating sets consist of $3$ involutions $σ$, $τ$, and $s_α$, where the latter involution is inspired by the class of spinal elements in the theory of branch groups. In particular this shows the existence of generating sets of $V_n$ that consist of $3$ involutions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2411.09069

Authors: Schesler, Eduard, Skipper, Rachel, Wu, Xiaolei

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4404449887

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