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A geometric classification of some solvable groups of homeomorphisms
Author(s) -
Bleak Collin
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn017
Subject(s) - mathematics , wreath product , solvable group , combinatorics , finitely generated abelian group , product (mathematics) , piecewise , piecewise linear function , group (periodic table) , orientation (vector space) , interval (graph theory) , pure mathematics , unit interval , mathematical analysis , geometry , abelian group , chemistry , organic chemistry
We investigate subgroups of the group PL o ( I ) of piecewise‐linear, orientation‐preserving homeomorphisms of the unit interval with finitely many breaks in slope, under the operation of composition, and also subgroups of generalized Thompson groups F n . We find geometric criteria determining the derived length of any such group, and use these criteria to produce a geometric classification of the solvable and non‐solvable subgroups of PL o ( I ) and of the F n . We also show that any standard restricted wreath product (of non‐trivial groups) that embeds in PL o ( I ) or F n must have T ≅ ℤ.