A short proof that positive generation implies the Hanna Neumann Conjecture

TL;DR

This paper presents a concise proof demonstrating that positively generated subgroups of free groups cannot serve as counterexamples to the Generalized Hanna Neumann Conjecture, simplifying the understanding of the conjecture's constraints.

Contribution

The paper provides a short, elegant proof linking positive generation of subgroups to the validity of the Hanna Neumann Conjecture.

Findings

Positively generated subgroups cannot be counterexamples

The proof is notably concise and straightforward

Supports the conjecture's validity in specific cases

Abstract

We give a very short proof that a subgroup of a free group that is positively generated cannot be part of a counterexample to the Generalized Hanna Neumann Conjecture.