About isolators of finitely generated subgroups of free groups

TL;DR

This paper provides a simple proof that in free groups, the isolator of any finitely generated subgroup is itself finitely generated, clarifying a known property with an accessible demonstration.

Contribution

The paper introduces a straightforward proof of a known result about the finite generation of isolators in free groups.

Findings

Proves that isolators of finitely generated subgroups in free groups are finitely generated

Simplifies the understanding of subgroup properties in free groups

Enhances the theoretical framework of free group subgroup analysis

Abstract

It is known that in any free group the isolator of finitely generated subgroup is finitely generated subgroup. A very simple proof of this statement is proposed.