Geodesic
A minimal non-solvable group of homeomorphisms
Collin Bleak1 orcid
1University of St Andrews, United Kingdom
Groups, geometry, and dynamics, Tome 3 (2009) no. 1, pp. 1-37

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DOI

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). 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​.
DOI : 10.4171/ggd/50
Classification : 20-XX, 37-XX, 00-XX
Mots-clés : PL homeomorphisms, group actions, unit interval, non-solvable groups, Thompson's group <var>F<var>

Collin Bleak  1

1 University of St Andrews, United Kingdom 
Collin Bleak. A minimal non-solvable group of homeomorphisms. Groups, geometry, and dynamics, Tome 3 (2009) no. 1, pp. 1-37. doi: 10.4171/ggd/50
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