On properties not inherited by monoids from their Schützenberger groups

Gray, R., Malheiro, A. and Pride, S. J. (2011) On properties not inherited by monoids from their Schützenberger groups. Information and Computation, 209 (7). pp. 1120-1134.

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Abstract

We give an example of a monoid with finitely many left and right ideals, all of whose Schützenberger groups are presentable by finite complete rewriting systems, and so each have finite derivation type, but such that the monoid itself does not have finite derivation type, and therefore does not admit a presentation by a finite complete rewriting system. The example also serves as a counterexample to several other natural questions regarding complete rewriting systems and finite derivation type. Specifically it allows us to construct two finitely generated monoids M and N with isometric Cayley graphs, where N has finite derivation type (respectively, admits a presentation by a finite complete rewriting system) but M does not. This contrasts with the case of finitely generated groups for which finite derivation type is known to be a quasi-isometry invariant. The same example is also used to show that neither of these two properties is preserved under finite Green index extensions.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Users 2731 not found.
Date Deposited:	21 Feb 2013 21:16
Last Modified:	07 Nov 2024 12:32
URI:	https://ueaeprints.uea.ac.uk/id/eprint/41513
DOI:	10.1016/j.ic.2011.03.004

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