Volume 14, issue 1 (2014)

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A weak Zassenhaus Lemma for discrete subgroups of $\operatorname{Diff}(I)$

Azer Akhmedov

Algebraic & Geometric Topology 14 (2014) 539–550
Abstract

We prove a weaker version of the Zassenhaus Lemma for subgroups of $Diff\left(I\right)$. We also show that a group with commutator subgroup containing a non-Abelian free subsemigroup does not admit a ${C}_{0}$–discrete faithful representation in $Diff\left(I\right)$.

Keywords
diffeomorphism group of the interval, Zassenhaus Lemma, discrete subgroups of $\operatorname{Diff}(I)$
Primary: 37C05
Secondary: 20F65