On isomorphisms to a free group and beyond

TL;DR

This paper explores the complex problem of determining isomorphisms to free and limit groups, addressing algorithmic challenges in classifying and embedding finitely presented groups within these classes.

Contribution

It advances understanding of isomorphism problems for specific classes of groups and proposes methods for embedding finitely presented groups into limit groups.

Findings

Solved isomorphism problems for certain classes like nilpotent and hyperbolic groups

Developed algorithms for embedding finitely presented groups into limit groups

Extended the scope of isomorphism analysis beyond free groups

Abstract

The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and limit groups. In this short paper, we address the problem of isomorphism to particular groups, including free groups. We also address the algorithmic problem of embedding a finitely presented group in a given limit group.