A combinatorial approach to rational exponential groups

TL;DR

This paper introduces rational complexes and demonstrates that every rational exponential group can be realized as the fundamental group of such a complex, establishing a new connection between algebraic and topological structures.

Contribution

It defines rational complexes and proves that all rational exponential groups are fundamental groups of these complexes, showing the variety is Schreier.

Findings

Every rational exponential group is a fundamental group of a rational complex.

The variety of rational exponential groups is Schreier.

Provides a new topological perspective on rational exponential groups.

Abstract

We give a suitable definition of the concept of rational complex and prove that every rational exponential group is the fundamental group of some such a complex. In this framework, we prove that the variety of rational exponential groups is a Schreier variety.