Monoid presentations of groups by finite special string-rewriting systems
Department of Mathematics and Computer
University of Leicester,
University Road, Leicester, LE1 7RH, England;
2 : School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland; firstname.lastname@example.org.
3 : IT-Universitetet i København, Glentevej 67, 2400 København NV, Denmark; email@example.com.
Accepted: 19 March 2004
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.
Mathematics Subject Classification: 20E06 / 20F05 / 20F10 / 68Q42
Key words: Group / monoid presentation / Cayley graph / special string-rewriting system / word problem.
© EDP Sciences, 2004