---
_id: '55192'
abstract:
- lang: eng
  text: "We describe the group of $\\mathbb Z$-linear automorphisms of the ring of\r\nintegers
    of a number field $K$ that preserve the set $V_{K,k}$ of $k$th\r\npower-free integers:
    every such map is the composition of a field automorphism\r\nand the multiplication
    by a unit.\r\n  We show that those maps together with translations generate the
    extended\r\nsymmetry group of the shift space $\\mathbb D_{K,k}$ associated to
    $V_{K,k}$.\r\nMoreover, we show that no two such dynamical systems $\\mathbb D_{K,k}$
    and\r\n$\\mathbb D_{L,l}$ are topologically conjugate and no one is a factor system
    of\r\nanother.\r\n  We generalize the concept of $k$th power-free integers to
    sieves and study\r\nthe resulting admissible shift spaces."
author:
- first_name: Fabian
  full_name: Gundlach, Fabian
  id: '100450'
  last_name: Gundlach
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Gundlach F, Klüners J. Symmetries of power-free integers in number fields and
    their shift  spaces. <i>arXiv:240708438</i>. Published online 2024.
  apa: Gundlach, F., &#38; Klüners, J. (2024). Symmetries of power-free integers in
    number fields and their shift  spaces. In <i>arXiv:2407.08438</i>.
  bibtex: '@article{Gundlach_Klüners_2024, title={Symmetries of power-free integers
    in number fields and their shift  spaces}, journal={arXiv:2407.08438}, author={Gundlach,
    Fabian and Klüners, Jürgen}, year={2024} }'
  chicago: Gundlach, Fabian, and Jürgen Klüners. “Symmetries of Power-Free Integers
    in Number Fields and Their Shift  Spaces.” <i>ArXiv:2407.08438</i>, 2024.
  ieee: F. Gundlach and J. Klüners, “Symmetries of power-free integers in number fields
    and their shift  spaces,” <i>arXiv:2407.08438</i>. 2024.
  mla: Gundlach, Fabian, and Jürgen Klüners. “Symmetries of Power-Free Integers in
    Number Fields and Their Shift  Spaces.” <i>ArXiv:2407.08438</i>, 2024.
  short: F. Gundlach, J. Klüners, ArXiv:2407.08438 (2024).
date_created: 2024-07-12T08:16:37Z
date_updated: 2024-07-12T08:19:11Z
external_id:
  arxiv:
  - '2407.08438'
language:
- iso: eng
publication: arXiv:2407.08438
status: public
title: Symmetries of power-free integers in number fields and their shift  spaces
type: preprint
user_id: '82981'
year: '2024'
...