The theorems on freedom for relatively free groups with a relations

TL;DR

This paper proves theorems on the freedom properties of relatively free groups with one relation, extending classical results by Magnus and Romanovski to a broader context.

Contribution

It introduces new theorems on the freedom of relatively free groups with a single relation and generalizes the Freiheitssatz for these groups.

Findings

Proved the theorem on freedom for relatively free groups with one relation.

Established a generalized Freiheitssatz for relatively free groups.

Extended classical results to a broader class of groups.

Abstract

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