Abstract
We compute the dimension group of the skew product extension of a Cantor minimal system associated with a finite group valued cocycle. Using it, we study finite subgroups in the commutant group of a Cantor minimal system and prove that a finite subgroup of the kernel of the mod map must be cyclic. Moreover, we give a certain obstruction for finite subgroups of commutant groups to have nonzero intersection to the kernel of mod maps. We also give a necessary and sufficient condition for dimension groups so that the kernel of the mod map can include a finite order element.
Citation
Hiroki MATUI. "Finite order automorphisms and dimension groups of Cantor minimal systems." J. Math. Soc. Japan 54 (1) 135 - 160, January, 2002. https://doi.org/10.2969/jmsj/1191593958
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