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FOR REWRITING SYSTEMS THE TOPOLOGICAL FINITENESS CONDITIONS FDT AND FHT ARE NOT EQUIVALENT

Published online by Cambridge University Press:  29 March 2004

STEPHEN J. PRIDE  and
FRIEDRICH OTTO
STEPHEN J. PRIDE
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW sjp@maths.gla.ac.uk
FRIEDRICH OTTO
Affiliation:
Fachbereich Mathematik/Informatik, Universität Kassel, 34109 Kassel, Germanyotto@theory.informatik.uni-kassel.de
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Abstract

A finite rewriting system is presented that does not satisfy the homotopical finiteness condition FDT, although it satisfies the homological finiteness condition FHT. This system is obtained from a group $G$ and a finitely generated subgroup $H$ of $G$ through a monoid extension that is almost an HNN extension. The FHT property of the extension is closely related to the ${\rm FP}_2$ property for the subgroup $H$, while the FDT property of the extension is related to the finite presentability of $H$. The example system separating the FDT property from the FHT property is then obtained by applying this construction to an example group.

Keywords

20J0620M50 (primary)20F3668Q42 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 363 - 382
Copyright
The London Mathematical Society 2004

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Footnotes

This work was supported by a grant from the EPSRC under the MathFIT 2000 initiative (grant GR/R29888).