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Abstract
Given a monoid defined by a presentation, and a homotopy base for the derivation graph associated to the presentation, and given an arbitrary subgroup of the monoid, we give a homotopy base (and presentation) for the subgroup. If the monoid has finite derivation type (FDT), and if under the action of the monoid on its subsets by right multiplication the strong orbit of the subgroup is finite, then we obtain a finite homotopy base for the subgroup, and hence the subgroup has FDT. As an application we prove that a regular monoid with finitely many left and right ideals has FDT if and only if all of its maximal subgroups have FDT. We use this to show that a finitely presented regular monoid with finitely many left and right ideals satisfies the homological finiteness condition FP3 if all of its maximal subgroups satisfy the condition FP3. (C) 2014 Elsevier Inc. All rights reserved.
Original language  English 

Pages (fromto)  5384 
Number of pages  32 
Journal  Journal of Algebra 
Volume  410 
DOIs  
Publication status  Published  15 Jul 2014 
Keywords
 Rewriting systems
 Finitely presented groups and monoids
 Finiteness conditions
 Homotopy bases
 Finite derivation type
 COMPLETE REWRITINGSYSTEMS
 CONDITION FP3
 SEMIGROUPS
 PRESENTATIONS
 EQUIVALENT
 IDEALS
 INDEX
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Dive into the research topics of 'Homotopy bases and finite derivation type for subgroups of monoids'. Together they form a unique fingerprint.Projects
 1 Finished

Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids
Gray, R. D.
1/02/08 → 31/01/11
Project: Standard