Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On subgroup growth of iterated wreath products in product action

Matteo Vannacci

Abstract

We show that there are hereditarily just infinite groups of any subgroup growth type between $n$ and $n^{\log n}$. This is obtained calculating the subgroup growth type of a family of hereditarily just infinite profinite groups obtained via iterated wreath products of finite permutation groups with respect to product actions.

On subgroup growth of iterated wreath products in product action

Abstract

We show that there are hereditarily just infinite groups of any subgroup growth type between and . This is obtained calculating the subgroup growth type of a family of hereditarily just infinite profinite groups obtained via iterated wreath products of finite permutation groups with respect to product actions.
Paper Structure (5 sections, 7 theorems, 19 equations)

This paper contains 5 sections, 7 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. State of the art
  3. Main result
  4. Nice sequences of groups
  5. Proof of Theorem \ref{['thm:A']}

Key Result

Theorem 1

Let $f:\mathbb{N}\rightarrow \mathbb{R}$ be a gently growing function. Then there exists a sequence $(p_k)_{k\in \mathbb{N}}$ of primes such that the infinitely iterated wreath product of type $\mathcal{P} = \{\mathrm{PSL}_2(\mathbb{F}_{p_k})\}_{k\in \mathbb{N}}$ w.r.t. product actions, with $\mathr

Theorems & Definitions (15)

  • Theorem 1
  • Corollary 2
  • Definition 2.1
  • Remark 2.2
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • ...and 5 more