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

S. Bezuglyi, K. Medynets (2008)

Colloquium Mathematicae

We consider the full group [φ] and topological full group [[φ]] of a Cantor minimal system (X,φ). We prove that the commutator subgroups D([φ]) and D([[φ]]) are simple and show that the groups D([φ]) and D([[φ]]) completely determine the class of orbit equivalence and flip conjugacy of φ, respectively. These results improve the classification found in [GPS]. As a corollary of the technique used, we establish the fact that φ can be written as a product of three involutions from [φ].

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