Cyclic splittings of pro-p groups

TL;DR

This paper extends classical theorems on group splittings to the pro-p setting, providing new insights into how pro-p groups can be decomposed over infinite cyclic subgroups.

Contribution

It introduces a pro-p analogue of Rips-Sela's theorems, advancing the understanding of group splittings in the pro-p context.

Findings

Proves a pro-p version of Rips-Sela's theorems.

Establishes conditions for splittings over infinite cyclic subgroups.

Enhances the structural theory of pro-p groups.

Abstract

In this paper we prove a pro-p version of the Rips-Sela's Theorems on splittings of a group as an amalgamated free product or HNN-extension over an infinite cyclic subgroup.