Detecting Relatively Quasiconvex Subgroups and Their Induced Peripheral Structure

TL;DR

This paper introduces an algorithm that detects relatively quasiconvex subgroups within relatively hyperbolic groups and determines their induced peripheral structures, advancing understanding of subgroup structures in geometric group theory.

Contribution

The paper presents the first algorithmic method to identify relatively quasiconvex subgroups and compute their induced peripheral structures in relatively hyperbolic groups.

Findings

Algorithm exists under certain conditions

Detects relatively quasiconvex subgroups

Outputs induced peripheral structures

Abstract

This paper proves under certain conditions the existence of an algorithm, which detects relatively quasiconvex subgroups $H$ of relatively hyperbolic groups $(G,\mathbb{P})$. Additionally, this algorithm outputs an induced peripheral structure of $(G,\mathbb{P})$ on $H$.