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For Rewriting Systems the Topological Finiteness Conditions FDT and FHT are Not Equivalent
Author(s) -
Pride Stephen J.,
Otto Friedrich
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004903
Subject(s) - rewriting , extension (predicate logic) , mathematics , property (philosophy) , monoid , pure mathematics , group (periodic table) , free monoid , algebra over a field , computer science , physics , programming language , epistemology , philosophy , quantum mechanics
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 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.