A Minimal Non-solvable Group of Homeomorphisms
| dc.creator | Bleak, Collin | |
| dc.date | 2006-08-07 | |
| dc.date.accessioned | 2026-07-07T07:21:30Z | |
| dc.date.available | 2026-07-07T07:21:30Z | |
| dc.description | 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 $F_n$. | |
| dc.description | 29 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0608182 | |
| dc.identifier | http://arxiv.org/abs/math/0608182 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115320 | |
| dc.subject | Group Theory | |
| dc.subject | General Topology | |
| dc.subject | 20F38 | |
| dc.title | A Minimal Non-solvable Group of Homeomorphisms | |
| dc.type | text |