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Finite presentability and isomorphism of Cayley graphs of monoids


Authors: J. Awang, M. Pfeiffer and N. Ruškuc
Journal: Proc. Amer. Math. Soc. 145 (2017), 4585-4593
MSC (2010): Primary 20M05, 05C20
DOI: https://doi.org/10.1090/proc/13557
Published electronically: August 7, 2017
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Abstract: Two finitely generated monoids are constructed, one finitely presented, the other not, whose (directed, unlabelled) Cayley graphs are isomorphic.


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  • [1] Ronald V. Book and Friedrich Otto, String-rewriting systems, Texts and Monographs in Computer Science, Springer-Verlag, New York, 1993. MR 1215932
  • [2] Stanley Burris and H. P. Sankappanavar, A course in universal algebra, Graduate Texts in Mathematics, vol. 78, Springer-Verlag, New York-Berlin, 1981. MR 648287
  • [3] Martin R. Bridson and André Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999. MR 1744486
  • [4] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. II, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1967. MR 0218472
  • [5] Pierre de la Harpe, Topics in geometric group theory, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000. MR 1786869
  • [6] Robert Gray and Mark Kambites, A Švarc-Milnor lemma for monoids acting by isometric embeddings, Internat. J. Algebra Comput. 21 (2011), no. 7, 1135-1147. MR 2863430, https://doi.org/10.1142/S021819671100687X
  • [7] Robert Gray and Mark Kambites, Groups acting on semimetric spaces and quasi-isometries of monoids, Trans. Amer. Math. Soc. 365 (2013), no. 2, 555-578. MR 2995365, https://doi.org/10.1090/S0002-9947-2012-05868-5
  • [8] Robert D. Gray and Mark Kambites, Quasi-isometry and finite presentations of left cancellative monoids, Internat. J. Algebra Comput. 23 (2013), no. 5, 1099-1114. MR 3096313, https://doi.org/10.1142/S0218196713500185

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Additional Information

J. Awang
Affiliation: School of Mathematics and Statistics, University of St Andrews, St. Andrews, Scotland, United Kingdom
Email: jsa23@st-andrews.ac.uk

M. Pfeiffer
Affiliation: School of Computer Science, University of St Andrews, St. Andrews, Scotland, United Kingdom
Email: markus.pfeiffer@st-andrews.ac.uk

N. Ruškuc
Affiliation: School of Mathematics and Statistics, University of St Andrews, St. Andrews, Scotland, United Kingdom
Email: nik.ruskuc@st-andrews.ac.uk

DOI: https://doi.org/10.1090/proc/13557
Received by editor(s): February 25, 2016
Received by editor(s) in revised form: October 15, 2016
Published electronically: August 7, 2017
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2017 American Mathematical Society

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