On some maximal subgroups of the kernel of the index map associated with a minimal homeomorphism of the Cantor set

Abstract

If $T$ is a minimal homeomorphism of the Cantor set $X$, and $[[T]{]}_0$ is the kernel of the index map, we give a short proof of the characterization of the maximal subgroups $G$ of $[[T]{]}_0$ such that $G$ does not act minimally on $X$. They are stabilizers of nonempty closed subsets $Y$ of $X$, and we present a classification when $Y$ is finite.