Automatic groups and amalgams

DOI10.1016/0022-4049(91)90139-SzbMath0749.20006MaRDI QIDQ1183379

Gilbert Baumslag, Hamish Short, Steve M. Gersten, Michael Shapiro

Publication date: 28 June 1992

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

zbMATH Keywords

negatively curved groupsfree groupsamalgamated productsfinitely generated Abelian groupsasynchronously automatic groupscyclic amalgamations

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Free semigroups, generators and relations, word problems (20M05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06)

Related Items (52)

THE COMBINATION THEOREM AND QUASICONVEXITY ⋮ AUTOMATIC SEMIGROUPS WITH SUBSEMIGROUPS OF FINITE REES INDEX ⋮ An automatic semigroup of languages ⋮ Graph groups are biautomatic ⋮ Automaticity of one-relator semigroups with length less than or equal to three ⋮ AMALGAMATED PRODUCTS OF NONPOSITIVELY CURVED GROUPS WHICH DO NOT SATISFY THE QUADRATIC ISOPERIMETRIC INEQUALITY ⋮ Hyperbolicity of \(T(6)\) cyclically presented groups ⋮ The Development of the Theory of Automatic Groups ⋮ Automatic structures, rational growth, and geometrically finite hyperbolic groups ⋮ A geometric characterization of automatic semigroups ⋮ Free and fragmenting filling length. ⋮ Artin groups of extra-large type are biautomatic ⋮ Preservation and distortion of area in finitely presented groups ⋮ On restricted gromov groups ⋮ THE CONJUGACY PROBLEM IN AMALGAMATED PRODUCTS I: REGULAR ELEMENTS AND BLACK HOLES ⋮ Regularity of Morse geodesics and growth of stable subgroups ⋮ Generic-case complexity, decision problems in group theory, and random walks. ⋮ CSA-groups and separated free constructions ⋮ Topology, formal languages and quantum information ⋮ Geometry of the word problem for 3-manifold groups ⋮ Small cancellation groups and translation numbers ⋮ WORD EQUATIONS OVER GRAPH PRODUCTS ⋮ GENERIC COMPLEXITY OF THE CONJUGACY PROBLEM IN HNN-EXTENSIONS AND ALGORITHMIC STRATIFICATION OF MILLER'S GROUPS ⋮ The equivalence of some residual properties of word-hyperbolic groups ⋮ Automatic groups and amalgams ⋮ The geometry of the handlebody groups. II: Dehn functions ⋮ Automaticity for graphs of groups ⋮ Hyperbolic groups and free constructions ⋮ Subgroup properties of fully residually free groups ⋮ Automatic structures for semigroup constructions. ⋮ Automatic subsemigroups of free products. ⋮ Braid groups of imprimitive complex reflection groups. ⋮ Growth Functions for Some Nonautomatic Baumslag-Solitar Groups ⋮ Average-case complexity and decision problems in group theory. ⋮ Regular path systems and (bi)automatic groups. ⋮ AUTOMATIC STRUCTURES FOR FUNDAMENTAL GROUPOIDS OF GRAPHS OF GROUPS ⋮ Translation numbers in a Garside group are rational with uniformly bounded denominators. ⋮ Finite transducers for divisibility monoids ⋮ Finiteness and Dehn functions of automatic monoids having directed fellow traveller property. ⋮ Homology and closure properties of autostackable groups ⋮ Commensurating HNN extensions: nonpositive curvature and biautomaticity ⋮ Combings of semidirect products and 3-manifold groups ⋮ Small cancellation theory and automatic groups ⋮ Subsemigroups of groups: presentations, Malcev presentations, and automatic structures ⋮ The word problem for Artin groups of FC type ⋮ Mapping tori of endomorphisms of free groups ⋮ On the automaticity of singular Artin monoids of finite type ⋮ Automatic semigroups ⋮ GROWTH SERIES FOR ARTIN GROUPS OF DIHEDRAL TYPE ⋮ Extensions and submonoids of automatic monoids. ⋮ Small cancellation theory and automatic groups. II ⋮ Isoperimetric inequalities and the homology of groups

Cites Work

• Small cancellation theory and automatic groups
• A combination theorem for negatively curved groups
• Small cancellation theory and automatic groups. II
• Topology of finite graphs
• The combinatorial structure of cocompact discrete hyperbolic groups
• Rational subgroups of biautomatic groups
• Automatic groups and amalgams
• Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
• Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
• On Dehn's algorithm
• Some two-generator one-relator non-Hopfian groups
• On Group-Theoretic Decision Problems and Their Classification. (AM-68)
• Some results on one-relator groups
• The Subgroups of a Free Product of Two Groups with an Amalgamated Subgroup
• Coset Representations in Free Groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Automatic groups and amalgams