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].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-2-6,
author = {S. Bezuglyi and K. Medynets},
title = {Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems},
journal = {Colloquium Mathematicae},
volume = {111},
year = {2008},
pages = {409-429},
zbl = {1142.37011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-2-6}
}
S. Bezuglyi; K. Medynets. Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems. Colloquium Mathematicae, Tome 111 (2008) pp. 409-429. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-2-6/