Monoid presentations of groups by finite special string-rewriting systems
Parkes, Duncan W. ; Shavrukov, V. Yu. ; Thomas, Richard M.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004), p. 245-256 / Harvested from Numdam
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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.

Publié le : 2004-01-01
DOI : https://doi.org/10.1051/ita:2004012
Classification:  20E06,  20F05,  20F10,  68Q42 
@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},
     volume = {38},
     year = {2004},
     pages = {245-256},
     doi = {10.1051/ita:2004012},
     mrnumber = {2076402},
     zbl = {1071.20037},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2004__38_3_245_0}
}

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) pp. 245-256. doi : 10.1051/ita:2004012. http://gdmltest.u-ga.fr/item/ITA_2004__38_3_245_0/

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