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.

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We show that the class of groups which have monoid presentations by means of finite special [λ]-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 : 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},
     volume = {38},
     number = {3},
     year = {2004},
     doi = {10.1051/ita:2004012},
     zbl = {1071.20037},
     mrnumber = {2076402},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/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. https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2004012/

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