Monoid presentations of groups by finite special string-rewriting systems
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 3, pp. 245-256.

We show that the class of groups which have monoid presentations by means of finite special $\left[\lambda \right]$-confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and only if it is the direct product of an infinite cyclic group and a finite cyclic group.

DOI : https://doi.org/10.1051/ita:2004012
Classification : 20E06,  20F05,  20F10,  68Q42
Mots clés : group, monoid presentation, Cayley graph, special string-rewriting system, word problem
@article{ITA_2004__38_3_245_0,
author = {Parkes, Duncan W. and Shavrukov, V. Yu. and Thomas, Richard M.},
title = {Monoid presentations of groups by finite special string-rewriting systems},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {245--256},
publisher = {EDP-Sciences},
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url = {http://www.numdam.org/articles/10.1051/ita:2004012/}
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Parkes, Duncan W.; Shavrukov, V. Yu.; Thomas, Richard M. Monoid presentations of groups by finite special string-rewriting systems. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 3, pp. 245-256. doi : 10.1051/ita:2004012. http://www.numdam.org/articles/10.1051/ita:2004012/

[1] R.V. Book and F. Otto, String-Rewriting Systems. Texts and Monographs in Computer Science, Springer-Verlag (1993). | MR 1215932 | Zbl 0832.68061

[2] Y. Cochet, Church-Rosser congruences on free semigroups, in Algebraic Theory of Semigroups, edited by G. Pollák. Colloquia Mathematica Societatis János Bolyai 20, North-Holland Publishing Co. (1979) 51-60. | Zbl 0408.20054

[3] R.H. Haring-Smith, Groups and simple languages. Trans. Amer. Math. Soc. 279 (1983) 337-356. | Zbl 0518.20030

[4] T. Herbst and R.M. Thomas, Group presentations, formal languages and characterizations of one-counter groups. Theoret. Comput. Sci. 112 (1993) 187-213. | Zbl 0783.68066

[5] R.C. Lyndon and P.E. Schupp, Combinatorial Group Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete 89, Springer-Verlag (1977). | MR 577064 | Zbl 0368.20023

[6] K. Madlener and F. Otto, About the descriptive power of certain classes of finite string-rewriting systems. Theoret. Comput. Sci. 67 (1989) 143-172. | Zbl 0697.20017

[7] W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory, 2nd edn. Dover (1976). | MR 422434 | Zbl 0362.20023

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