A minimal non-solvable group of homeomorphisms

C Bleak*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

Let PLo(I) represent the group of orientation-preserving piecewise-linear homeomorphisms of the unit interval which admit finitely many breaks in slope, under the operation of composition. We find a non-solvable group W and show that W embeds in every non-solvable subgroup of PLo(I). We find mild conditions under which other non-solvable subgroups B, (≀ℤ≀)∞, (ℤ≀)∞, and ∞(≀ℤ) embed in subgroups of Let PLo(I) represent the group of orientation-preserving piecewise-linear homeomorphisms of the unit interval which admit finitely many breaks in slope, under the operation of composition. We find a non-solvable group W and show that W embeds in every non-solvable subgroup of PLo(I). We show that all solvable subgroups of PLo(I) embed in all non-solvable subgroups of PLo(I). These results continue to apply if we replace PLo(I) by any generalized Thompson group Fn.
Original languageEnglish
Pages (from-to)1-37
Number of pages37
JournalGroups, Geometry, and Dynamics
Volume3
Issue number1
DOIs
Publication statusPublished - 31 Mar 2009

Keywords

  • PL homeomorphisms
  • Thompson's group F
  • Group actions
  • Non-solvable groups
  • Unit interval

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