Homotopy bases and finite derivation type for subgroups of monoids

JOURNAL OF ALGEBRA

卷:410

Article

Gray, R. D.¹  Malheiro, A.^2,3 

[1] Univ E Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England

[2] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, P-2829516 Caparica, Portugal

[3] Univ Lisbon, Ctr Algebra, P-1649003 Lisbon, Portugal

关键词: Rewriting systems;    Finitely presented groups and monoids;    Finiteness conditions;    Homotopy bases;    Finite derivation type;   

DOI  :  10.1016/j.jalgebra.2014.03.035

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free