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Journal of the London Mathematical Society (1)

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FOR REWRITING SYSTEMS THE TOPOLOGICAL FINITENESS CONDITIONS FDT AND FHT ARE NOT EQUIVALENT
STEPHEN J. PRIDE, FRIEDRICH OTTO
Journal:

Journal of the London Mathematical Society / Volume 69 / Issue 2 / April 2004

Published online by Cambridge University Press:

29 March 2004, pp. 363-382

Print publication:

April 2004
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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.