Graph groups are biautomatic

DOI10.1016/0022-4049(94)90015-9zbMath0812.20018OpenAlexW1972761586MaRDI QIDQ1331906

Leonard Van Wyk

Publication date: 9 May 1995

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(94)90015-9

zbMATH Keywords

presentationgeneratorsnormal formsregular languagefree groupsrelationfree monoidgraph groupscombingsbiautomaticbicombablecommuting clique

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Topological methods in group theory (57M07) Automorphism groups of groups (20F28) Free nonabelian groups (20E05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Related Items (22)

Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups. ⋮ REWRITING SYSTEMS AND ORDERINGS ON ARTIN MONOIDS ⋮ The Development of the Theory of Automatic Groups ⋮ Geometry and Combinatorics via Right-Angled Artin Groups ⋮ An introduction to right-angled Artin groups. ⋮ Intersection problem for Droms RAAGs ⋮ Rigidity of graph products of groups. ⋮ Co-contractions of graphs and right-angled Artin groups. ⋮ Full-featured peak reduction in right-angled Artin groups. ⋮ Parabolic and quasiparabolic subgroups of free partially commutative groups. ⋮ On higher order homological finiteness of rewriting systems. ⋮ Rewriting Systems and Embedding of Monoids in Groups ⋮ Symplectic structures on right-angled Artin groups: between the mapping class group and the symplectic group. ⋮ Normal Forms for Basis-Conjugating Automorphisms of a Free Group ⋮ Fixed Points of Endomorphisms and Metrics in preGarside Monoids ⋮ On systems of equations over free partially commutative groups ⋮ The conjugacy problem in subgroups of right-angled Artin groups ⋮ Metric systolicity and two-dimensional Artin groups ⋮ Biautomatic structures in systolic Artin groups ⋮ The word problem for Artin groups of FC type ⋮ Artin groups, rewriting systems and three-manifolds ⋮ Homological conditions for graphical splittings of antisocial graph groups

Cites Work

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• Subgroups of graph groups
• Small cancellation theory and automatic groups
• Word problems and a homological finiteness condition for monoids
• The word problem for free partially commutative groups
• Automatic groups and amalgams
• Algorithms and geometry for graph products of groups
• Combinatorial problems of commutation and rearrangements
• On theories with a combinatorial definition of 'equivalence'
• Surface Subgroups of Graph Groups

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