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Multi-EGS-groups: exponent of congruence quotients

Elena Maini

Abstract

Given a multi-EGS-group $K$ acting on the $p$-adic rooted tree, where $p$ is any prime number, we compute the exponent of the congruence quotient $K_n= K/ \St_K(n)$ for all $n\ge 1$. The formula that we obtain for $\exp(K_n)$ only depends on $p$, $n$ and the periodicity of $K$.

Multi-EGS-groups: exponent of congruence quotients

Abstract

Given a multi-EGS-group acting on the -adic rooted tree, where is any prime number, we compute the exponent of the congruence quotient for all . The formula that we obtain for only depends on , and the periodicity of .
Paper Structure (3 sections, 12 theorems, 41 equations)

This paper contains 3 sections, 12 theorems, 41 equations.

Table of Contents

  1. Introduction
  2. Non-periodic multi-EGS-groups
  3. Periodic multi-EGS-groups

Key Result

Theorem A

Let $K$ be a multi-EGS-group. Then for every $n\ge 1$ where $\lfloor \frac{n+1}{2} \rfloor$ is the greatest integer number less than or equal to $\frac{n+1}{2}$.

Theorems & Definitions (15)

  • Definition 1
  • Definition 2
  • Theorem A
  • Lemma 1
  • Lemma 2
  • proof
  • Lemma 3
  • Proposition 4
  • Theorem 5
  • Lemma 6
  • ...and 5 more