An algebraic classification of some solvable groups of homeomorphisms

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20 Citations (Scopus)


We produce two separate algebraic descriptions of the isomorphism classes of the solvable subgroups of the group PLo(I) of piecewise-linear orientation-preserving homeomorphisms of the unit interval under the operation of composition, and also of the generalized R. Thompson groups F_n. The first description is as a set of isomorphism classes of groups which is closed under three algebraic operations, and the second is as the set of isomorphism classes of subgroups of a countable collection of easily described groups. We show the two descriptions are equivalent.
Original languageEnglish
Pages (from-to)1368-1397
Number of pages30
JournalJournal of Algebra
Issue number4
Publication statusPublished - 15 Feb 2008


  • Solvable group
  • Infinite group
  • R. Thompson group
  • Homeomorphisms
  • Piecewise-linear


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