A minimal non-solvable group of homeomorphisms

  • Collin Bleak

    University of St Andrews, United Kingdom


Let 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 and show that embeds in every non-solvable subgroup of . We find mild conditions under which other non-solvable subgroups , , , and embed in subgroups of Let . We show that all solvable subgroups of embed in all non-solvable subgroups of PLo(I). These results continue to apply if we replace by any generalized Thompson group .

Cite this article

Collin Bleak, A minimal non-solvable group of homeomorphisms. Groups Geom. Dyn. 3 (2009), no. 1, pp. 1–37

DOI 10.4171/GGD/50