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Measuring Closeness Between Cayley Automatic Groups and Automatic Groups

  • Dmitry Berdinsky
  • Phongpitak Trakuldit
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10792)

Abstract

In this paper we introduce a way to estimate a level of closeness of Cayley automatic groups to the class of automatic groups using a certain numerical characteristic. We characterize Cayley automatic groups which are not automatic in terms of this numerical characteristic and then study it for the lamplighter group, the Baumslag–Solitar groups and the Heisenberg group.

Keywords

Automatic groups Cayley automatic groups Automatic structures Numerical characteristics of groups Lamplighter group Heisenberg group Baumslag–Solitar groups 
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Notes

Acknowledgments

The authors thank the referees for useful comments.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceMahidol UniversityBangkokThailand
  2. 2.Centre of Excellence in MathematicsCommission on Higher EducationBangkokThailand

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