On Tame Subgroups of Finitely Presented Groups

TL;DR

This paper investigates the properties of tame subgroups within finitely presented groups, establishing that their free products retain local tameness and providing numerous examples and open problems in the area.

Contribution

It proves that the free product of two finitely presented locally tame groups is also locally tame and offers many examples of tame subgroups, advancing understanding of their structure.

Findings

Free product of two finitely presented locally tame groups is locally tame

Provides numerous examples of tame subgroups of finitely presented groups

Includes open problems related to tame subgroups

Abstract

We prove that the free product of two finitely presented locally tame groups is locally tame and describe many examples of tame subgroups of finitely presented groups. We also include some open problems related to tame subgroups.