The theorems on freedom for free products with a relations

TL;DR

This paper proves theorems related to the freedom properties of free products with one relation and extends the Freiheitssatz to more general free products, advancing algebraic understanding of these structures.

Contribution

It introduces new theorems on freedom for free products with relations and generalizes the Freiheitssatz, building on classical results by Magnus and Romanovski.

Findings

Proved the theorem on freedom for free products with a single relation

Established a generalized Freiheitssatz for free products

Extended classical algebraic results to broader contexts

Abstract

In this paper we prove the theorem on freedom for free products with a single relation (analogous with the well-known result of Magnus) and a generalized Freiheitssatz for free products (analogous with the well-known result of Romanovski)