License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.131
URN: urn:nbn:de:0030-drops-91359
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9135/
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Klimann, Ines

To Infinity and Beyond

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LIPIcs-ICALP-2018-131.pdf (0.4 MB)

Abstract

We prove that if a group generated by a bireversible Mealy automaton contains an element of infinite order, then it must have exponential growth. As a direct consequence, no infinite virtually nilpotent group can be generated by a bireversible Mealy automaton.

BibTeX - Entry

@InProceedings{klimann:LIPIcs:2018:9135,
  author =	{Ines Klimann},
  title =	{{To Infinity and Beyond}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{131:1--131:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9135},
  URN =		{urn:nbn:de:0030-drops-91359},
  doi =		{10.4230/LIPIcs.ICALP.2018.131},
  annote =	{Keywords: automaton groups, growth of a group, exponential growth}
}

Keywords: automaton groups, growth of a group, exponential growth
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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