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Monoid presentations of groups by finite special string-rewritingsystems

Published online by Cambridge University Press:  15 June 2004

Duncan W. Parkes ,
V. Yu. Shavrukov  and
Richard M. Thomas
Duncan W. Parkes
Affiliation:
Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, England; rmt@mcs.le.ac.uk. : School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland; dparkes@mcs.st-and.ac.uk.
V. Yu. Shavrukov
Affiliation:
Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, England; rmt@mcs.le.ac.uk. : IT-Universitetet i København, Glentevej 67, 2400 København NV, Denmark; volodya@itu.dk.
Richard M. Thomas
Affiliation:
Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, England; rmt@mcs.le.ac.uk.
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Abstract

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.

Keywords

Groupmonoid presentationCayley graphspecial string-rewriting systemword problem.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 38 , Issue 3 , July 2004 , pp. 245 - 256
Copyright
© EDP Sciences, 2004

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References

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