LENGTH AND AREA FUNCTIONS ON GROUPS AND QUASI-ISOMETRIC HIGMAN EMBEDDINGS

DOI10.1142/S0218196701000401zbMath1025.20030arXivmath/9811107OpenAlexW2131739013MaRDI QIDQ4786274

Mark V. Sapir, Alexander Yu. Ol'shanskii

Publication date: 15 December 2002

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9811107

zbMATH Keywords

word problemfinitely presented groupslength functionsisoperimetric functionsDehn functionsvan Kampen diagrams

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Asymptotic properties of groups (20F69) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Related Items (18)

Solvable groups with polynomial Dehn functions ⋮ Polynomially-bounded Dehn functions of groups ⋮ Hyperplanes of Squier's cube complexes ⋮ GROUPS WITH QUADRATIC-NON-QUADRATIC DEHN FUNCTIONS ⋮ Algorithmically complex residually finite groups ⋮ Groups finitely presented in Burnside varieties ⋮ Endomorphic presentations of branch groups. ⋮ One-way permutations, computational asymmetry and distortion. ⋮ THE GROUPS OF RICHARD THOMPSON AND COMPLEXITY ⋮ The conjugacy problem for groups, and Higman embeddings ⋮ Groups with decidable word problem that do not embed in groups with decidable conjugacy problem ⋮ CIRCUITS, THE GROUPS OF RICHARD THOMPSON, AND coNP-COMPLETENESS ⋮ DEHN FUNCTION AND LENGTH OF PROOFS ⋮ Groups whose word problems are not semilinear ⋮ Divergence of finitely presented groups ⋮ Space functions of groups ⋮ Knapsack problems in groups ⋮ Asymptotic invariants, complexity of groups and related problems

Cites Work

• Groups of piecewise linear homeomorphisms of the real line
• Pseudo-natural algorithms for the word problem for finitely presented monoids and groups
• On finitely generated soluble linear groups
• On the asymptotic cone of groups satisfying a quadratic isoperimetric inequality
• Preservation and distortion of area in finitely presented groups
• The Extrinsic Geometry of Subgroups and the Generalized Word Problem
• Time-Complexity of the Word Problem for Semigroups and the Higman Embedding Theorem
• Finitely Presented Subgroups of Automatic Groups and their Isoperimetric Functions
• Subgroups of Direct Products of Free Groups

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