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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel


IMPACT FACTOR 2018: 0.536

CiteScore 2018: 0.83

SCImago Journal Rank (SJR) 2018: 1.041
Source Normalized Impact per Paper (SNIP) 2018: 0.801

Mathematical Citation Quotient (MCQ) 2017: 0.86

Open Access
Online
ISSN
2299-3274
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Geometry of Generated Groups with Metrics Induced by Their Cayley Color Graphs

Teerapong Suksumran
  • Corresponding author
  • Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
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Published Online: 2019-03-22 | DOI: https://doi.org/10.1515/agms-2019-0002

Abstract

Let G be a group and let S be a generating set of G. In this article,we introduce a metric dC on G with respect to S, called the cardinal metric.We then compare geometric structures of (G, dC) and (G, dW), where dW denotes the word metric. In particular, we prove that if S is finite, then (G, dC) and (G, dW) are not quasiisometric in the case when (G, dW) has infinite diameter and they are bi-Lipschitz equivalent otherwise. We also give an alternative description of cardinal metrics by using Cayley color graphs. It turns out that colorpermuting and color-preserving automorphisms of Cayley digraphs are isometries with respect to cardinal metrics.

Keywords: Cardinal metric; Cayley graph; Color-permuting automorphism; Color-preserving automorphism; Isometry of metric space

MSC 2010: Primary 20F65; Secondary 05C25, 05C12, 20F38

References

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About the article

Received: 2018-08-13

Accepted: 2019-02-17

Published Online: 2019-03-22

Published in Print: 2019-03-01


Citation Information: Analysis and Geometry in Metric Spaces, Volume 7, Issue 1, Pages 15–21, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2019-0002.

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© 2019 Teerapong Suksumran, published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. BY 4.0

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