On the height of subgroups of Homeo(I)

preprint2014arXivOpen access

In [Bl1], it is proved that a subgroup of $PL_{+}(I)$ has a finite height if and only if it is solvable. We prove the "only if" part for any subgroup of Homeo $_{+}(I)$ , and present a construction which indicates a plethora of examples of solvable groups with infinite height.

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On the height of subgroups of Homeo(I)

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