Yet another Freiheitssatz: Mating finite groups with locally indicable ones

TL;DR

This paper extends classical theorems in group theory by unifying and generalizing results related to the Freiheitssatz, focusing on the properties of finite and locally indicable groups.

Contribution

It introduces a new framework that generalizes several key theorems in group theory, including the Gerstenhaber--Rothaus, Nitsche--Thom, and Brodskii--Howie--Short theorems.

Findings

Unified framework for Freiheitssatz generalizations

Extension of classical theorems to broader classes of groups

New proofs and insights into group embeddings and properties

Abstract

The main result includes as special cases on the one hand, the Gerstenhaber--Rothaus theorem (1962) and its generalisation due to Nitsche and Thom (2022) and, on the other hand, the Brodskii--Howie--Short theorem (1980--1984) generalising Magnus's Freiheitssatz (1930).