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Cyclic splittings of pro-p groups

Jesus Berdugo, Pavel Zalesskii

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.

Cyclic splittings 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.
Paper Structure (11 sections, 21 theorems, 19 equations)

This paper contains 11 sections, 21 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Basic definitions
  4. Free pro-$p$ products with amalgamation
  5. $\mathbb{Z}_{p}$-splittings
  6. Normalizer
  7. Cyclic amalgamation
  8. Excluding Hyperbolic-Elliptic $\mathbb{Z}_{p}$-Splitting
  9. Hyperbolic-Hyperbolic $\mathbb{Z}_p$-splitting
  10. $p>2$
  11. $p=2$

Key Result

Theorem 1.2

Let $G$ be a finitely generated freely indecomposable pro-$p$ group. Then any two $\mathbb{Z}_{p}$-splittings of $G$ are either elliptic-elliptic or hyperbolic-hyperbolic.

Theorems & Definitions (41)

  • Definition 1.1
  • Theorem 1.2
  • Proposition 1.3
  • Theorem 1.4
  • Corollary 1.5
  • Theorem 1.6
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • ...and 31 more