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On the simplicity of the full group of ergodic transformations

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Abstract

LetE denote an invertible, non-singular, ergodic transformation of (0, 1). Then the full group ofE is perfect. IfE preserves the Lebesgue measure, then the full group is simple. IfE preserves no measure equivalent to Lebesgue, then the full group is simple. IfE preserves an infinite measure, then there exists a unique normal subgroup. IfT is any invertible transformation preserving the Lebesgue measure, then the full group is simple if and only ifT is ergodic on its support.

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Authors and Affiliations

  1. Department of Mathematics, McGill University, Burnside Hall, 805 Sherbrooke Street West, H3A 2K6, Montreal, Quebec, Canada

    S. J. Eigen

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  1. S. J. Eigen
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Eigen, S.J. On the simplicity of the full group of ergodic transformations. Israel J. Math. 40, 345–349 (1981). https://doi.org/10.1007/BF02761375

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  • DOI: https://doi.org/10.1007/BF02761375

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