A Minimal Non-solvable Group of Homeomorphisms

Details A Minimal Non-solvable Group of Homeomorphisms A Minimal Non-solvable Group of Homeomorphisms

2006-08-07

arxiv.org/abs/math/0608182v1

Mathematics

Group Theory

29 pages, 1 figure

Scientific paper

Let $PL_0(I)$ 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 $PL_0(I)$. We find mild conditions under which other non-solvable subgroups ($B$, $(\wr\Z\wr)^{\infty}$, $(\Z\wr)^{\infty}$, and $^{\infty}(\wr\Z)$) embed in subgroups of $PL_0(I)$. We show that all solvable subgroups of $PL_0(I)$ embed in all non-solvable subgroups of $PL_0(I)$. These results continue to apply if we replace $PL_0(I)$ by any generalized R. Thompson group $F_n$.

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