Supersolvable closures of finitely generated subgroups of the free group

Abstract

Abstract We prove that the pro-(finite supersolvable) closure of a finitely generated subgroup of the free group is finitely generated. This extends similar results for pro-𝑝 closures proved by Ribes–Zalesskii and pro-(finite nilpotent) closures proved by Margolis–Sapir–Weil.