The Extrinsic Geometry of Subgroups and the Generalized Word Problem

DOI10.1112/plms/s3-68.3.577zbMath0816.20032OpenAlexW1973933705MaRDI QIDQ4295865

Benson Farb

Publication date: 17 July 1995

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/plms/s3-68.3.577

zbMATH Keywords

solvable generalized word problemdistortion functionfinitely generated groupfinitely generated subgroupsolvable word problemoccurrence problemgeneralized isodiametric functionsgeneralized isoperimetric functionsquasiconvexity functionrecursive word problem

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

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Quadratic divergence of geodesics in CAT(0) spaces ⋮ ON DEHN FUNCTIONS OF AMALGAMATIONS AND STRONGLY UNDISTORTED SUBGROUPS ⋮ LENGTH AND AREA FUNCTIONS ON GROUPS AND QUASI-ISOMETRIC HIGMAN EMBEDDINGS ⋮ Extendability of Large-Scale Lipschitz Maps ⋮ Solvable groups with polynomial Dehn functions ⋮ Centralizers in the R. Thompson group \(V_n\). ⋮ Hyperbolic hydra. ⋮ Preservation and distortion of area in finitely presented groups ⋮ Nielsen generating sets and quasiconvexity of subgroups ⋮ Algorithmically complex residually finite groups ⋮ Volume distortion in groups. ⋮ Subgroup distortion in wreath products of cyclic groups. ⋮ Height in splittings of hyperbolic groups. ⋮ One-way permutations, computational asymmetry and distortion. ⋮ Quasi-isometrically embedded free sub-semigroups. ⋮ On intersections of conjugate subgroups ⋮ Exponential radicals of solvable Lie groups ⋮ On the geometry of infinite cyclic subgroups. ⋮ Relative subgroup growth and subgroup distortion

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