| Issue |
RAIRO-Theor. Inf. Appl.
Volume 38, Number 3, July-September 2004
|
|
|---|---|---|
| Page(s) | 245 - 256 | |
| DOI | https://doi.org/10.1051/ita:2004012 | |
| Published online | 15 June 2004 | |
Monoid presentations of groups by finite special string-rewriting systems
1
Department of Mathematics and Computer
Science,
University of Leicester,
University Road, Leicester, LE1 7RH, England;
rmt@mcs.le.ac.uk.
2
: School of Mathematics and
Statistics,
University of St Andrews,
St Andrews, KY16 9SS, Scotland; dparkes@mcs.st-and.ac.uk.
3
:
IT-Universitetet i København, Glentevej 67, 2400 København NV,
Denmark;
volodya@itu.dk.
Received:
19
September
2000
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
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