ELEMENTARY AMENABLE SUBGROUPS OF R. THOMPSON'S GROUP F

DOI10.1142/S0218196705002517zbMath1110.20018arXivmath/0501085OpenAlexW3103752413MaRDI QIDQ5703665

Matthew G. Brin

Publication date: 8 November 2005

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

Full work available at URL: https://arxiv.org/abs/math/0501085

zbMATH Keywords

amenabilitysolvable subgroupsThompson groupselementary amenable subgroups

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Subgroup theorems; subgroup growth (20E07) Generalizations of solvable and nilpotent groups (20F19) Other classes of groups defined by subgroup chains (20F22) Topological methods in group theory (57M07) Extensions, wreath products, and other compositions of groups (20E22) Topological properties of groups of homeomorphisms or diffeomorphisms (57S05) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items

A quasi-isometric embedding theorem for groups., On the dimension growth of groups., On the stabilizers of finite sets of numbers in the R. Thompson group $F$, The Generation Problem in Thompson Group 𝐹, On subgroups of R. Thompson’s group $F$, SOME GROUP THEORY PROBLEMS, Complexity among the finitely generated subgroups of Thompson's group, Groups of fast homeomorphisms of the interval and the ping-pong argument, An algebraic classification of some solvable groups of homeomorphisms., Numerical studies of Thompson’s group F and related groups, Determining solubility for finitely generated groups of PL homeomorphisms, A minimal non-solvable group of homeomorphisms., Random generation of Thompson group \(F\), Locally solvable subgroups of PLo(I) are countable, Distortion in groups of affine interval exchange transformations, Free products in R. Thompson’s group 𝑉, Elementary totally disconnected locally compact groups, Questions and remarks on discrete and dense subgroups of Diff(I)

Cites Work

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• The structure group for the associativity identity
• The characterization of generalized wreath products
• Wreath products of ordered permutation groups
• On the structure of standard wreath products of groups
• Metrics and embeddings of generalizations of Thompson’s group $F$
• The Ubiquity of Thompson's Group F in Groups of Piecewise Linear Homeomorphisms of the Unit Interval
• Finiteness properties of groups