A Minimal Non-solvable Group of Homeomorphisms

2006/08/07 by Bleak, Collin
#20F38 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0608182

Abstract

Let PL₀(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 PL₀(I). We find mild conditions under which other non-solvable subgroups (B, (\wr\Z\wr)^∞, (\Z\wr)^∞, and ^∞(\wr\Z)) embed in subgroups of PL₀(I). We show that all solvable subgroups of PL₀(I) embed in all non-solvable subgroups of PL₀(I). These results continue to apply if we replace PL₀(I) by any generalized R. Thompson group F_n.

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