A sufficient condition for accessibility of pro-$p$ groups

TL;DR

This paper provides a new criterion based on the module of ends' finite generation to determine when finitely generated pro- groups are accessible, advancing understanding of their structural properties.

Contribution

It introduces a sufficient condition for accessibility of pro- groups, linking it to the finite generation of the module of ends, which is a novel approach.

Findings

Established a sufficient condition for accessibility.

Connected accessibility to the finite generation of the module of ends.

Enhanced understanding of pro- group structure.

Abstract

We establish a sufficient condition for a finitely generated pro-$p$ group to be accessible in terms of finite generation of the module of ends.