Prosoluble subgroups of the profinite completion of the fundamental group of compact 3-manifolds

TL;DR

This paper characterizes finitely generated prosoluble subgroups within the profinite completions of 3-manifold groups and related classes, enhancing understanding of their algebraic structure.

Contribution

It provides a detailed description of prosoluble subgroups in the profinite completions of 3-manifold and virtually compact special groups, a novel structural insight.

Findings

Finitely generated prosoluble subgroups are explicitly described.

Results apply to profinite completions of 3-manifold groups.

Advances understanding of subgroup structures in profinite completions.

Abstract

We give a description of finitely generated prosoluble subgroups of the profinite completion of $3$-manifold groups and virtually compact special groups.