Semi-free subgroups of a profinite surface group

TL;DR

The paper proves that in a profinite surface group, every closed normal subgroup of infinite index is contained within a semi-free profinite normal subgroup, addressing a specific open question.

Contribution

It establishes a new structural property of profinite surface groups by linking infinite index normal subgroups to semi-free subgroups.

Findings

Every closed normal subgroup of infinite index is contained in a semi-free profinite normal subgroup.

Answers an open question posed by Bary-Soroker, Stevenson, and Zalesskii.

Advances understanding of subgroup structure in profinite surface groups.

Abstract

We show that every closed normal subgroup of infinite index in a profinite surface group $\Gamma$ is contained in a semi-free profinite normal subgroup of $\Gamma$. This answers a question of Bary-Soroker, Stevenson, and Zalesskii.