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

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 $Diff\left(I\right)$.