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special string-rewriting system

RAIRO - Theoretical Informatics and Applications (1)

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Monoid presentations of groups by finite special string-rewriting systems
Duncan W. Parkes, V. Yu. Shavrukov, Richard M. Thomas
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 38 / Issue 3 / July 2004

Published online by Cambridge University Press:

15 June 2004, pp. 245-256

Print publication:

July 2004
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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.