Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems

Abstract

We consider the full group $[\varphi ]$ and topological full group $[[\varphi ]]$ of a Cantor minimal system $(X,\varphi )$. We prove that the commutator subgroups $D([\varphi ])$ and $D([[\varphi ]])$ are simple and show that the groups $D([\varphi ])$ a