Homotopy bases and finite derivation type for subgroups of monoids.

DOI10.1016/j.jalgebra.2014.03.035zbMath1334.20055arXiv0912.1284OpenAlexW2132748257MaRDI QIDQ403106

António Malheiro, Robert D. Gray

Publication date: 29 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.1284

zbMATH Keywords

finitely presented groupsrewriting systemsfiniteness conditionsfinitely presented monoidsfinite derivation typehomotopy bases

Mathematics Subject Classification ID

Free semigroups, generators and relations, word problems (20M05) Semigroups in automata theory, linguistics, etc. (20M35) Grammars and rewriting systems (68Q42) Connections of semigroups with homological algebra and category theory (20M50)

Related Items (4)

Finite complete rewriting systems for regular semigroups. ⋮ Homological finiteness properties of monoids, their ideals and maximal subgroups. ⋮ Groups acting on semimetric spaces and quasi-isometries of monoids ⋮ On properties not inherited by monoids from their Schützenberger groups.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homological finiteness properties of monoids, their ideals and maximal subgroups.
• For groups the property of having finite derivation type is equivalent to the homological finiteness condition \(FP_ 3\)
• Green index and finiteness conditions for semigroups.
• Finitely approximable regular semigroups
• Syntactic and Rees indices of subsemigroups
• Finite complete rewriting systems and finite derivation type for small extensions of monoids
• A finiteness condition for rewriting systems
• Finite derivation type implies the homological finiteness condition \(FP_ 3\)
• Finite homotopy bases of one-relator monoids
• Combinatorial group theory.
• Presentations for subgroups of monoids
• A topological approach to inverse and regular semigroups.
• A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier)
• Finite derivation type for Rees matrix semigroups
• Finite derivation type for large ideals.
• Finite derivation type for semigroups and congruences.
• The index of a group in a semigroup
• On the structure of semigroups
• Constructions and presentations for monoids
• On the Algebra of Semigroup Diagrams
• Diagram groups
• SECOND ORDER DEHN FUNCTIONS OF GROUPS AND MONOIDS
• FOR REWRITING SYSTEMS THE TOPOLOGICAL FINITENESS CONDITIONS FDT AND FHT ARE NOT EQUIVALENT
• LOW-DIMENSIONAL HOMOTOPY THEORY FOR MONOIDS

This page was built for publication: Homotopy bases and finite derivation type for subgroups of monoids.