Abstract
This note answers a question of Kechris: if H < G is a normal subgroup of a countable group G, H has property MD and G/H is amenable and residually finite, then G also has property MD. Under the same hypothesis we prove that for any action a of G, if b is a free action of G/H, and b G is the induced action of G, then CInd G H (a|H) × b G weakly contains a. Moreover, if H < G is any subgroup of a countable group G, and the action of G on G/H is amenable, then CInd G H (a|H) weakly contains a whenever a is a Gaussian action.
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References
M. Abért and G. Elek, Dynamical properties of profinite actions, Ergodic Theory and Dynamical Systems, to appear.
M. Abért and B. Weiss, Bernoulli actions are weakly contained in any free action, Ergodic Theory and Dynamical Systems, to appear.
B. Bekka, P. de la Harpe and A. Valette, Kazhdan’s Property (T), New Mathematical Monographs, 11, Cambridge University Press, Cambridge, 2008.
L. Bowen, Periodicity and packings of the hyperbolic plane, Geometriae Dedicata 102 (2003), 213–236.
E. Glasner, J.-P. Thouvenot and B. Weiss, Every countable group has the weak Rohlin property, The Bulletin of the London Mathematical Society 38 (2006), 932–936.
A. Ioana, Non-orbit equivalent actions of \(\mathbb{F}_n\), Annales Scientifiques de l’École Normale Supérieure 42 (2009), 675–696.
A. Ioana, Orbit inequivalent actions for groups containing a copy of \(\mathbb{F}_2\), Inventiones Mathematicae 185 (2011), 55–73.
A. Kechris, Global Aspects of Ergodic Group Actions, Mathematical Surveys and Monographs, 160, American Mathematical Society, Providence, RI, 2010, xii+237 pp.
A. Kechris, Weak containment in the space of actions of a free group, Israel Journal of Mathematics, to appear.
A. Kechris and T. Tsankov, Amenable actions and almost invariant sets, Proceedings of the American Mathematical Society 136 (2008), 687–697.
A. Lubotzky and Y. Shalom, Finite representations in the unitary dual and Ramanujan groups, Contemporary Mathematics 347 (2004), 173–189.
A. Lubotzky and A. Zuk, On property (τ), preprint, 2003 (posted in http://www.ma.huji.ac.il/~alexlub/, 2003).
J. M. Ollagnier, Ergodic Theory and Statistical Mechanics, Lecture Notes inMathematics 1115, Springer-Verlag, Berlin, 1985, vi+147 pp.
D. S. Ornstein and B. Weiss, Ergodic theory of amenable group actions. I. The Rohlin lemma, American Mathematical Society. Bulletin 2 (1980), 161–164.
R. J. Zimmer, Ergodic Theory and Semisimple Groups, Monographs in Mathematics, 81, Birkhäuser Verlag, Basel, 1984.
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Bowen, L., Tucker-Drob, R.D. On a co-induction question of Kechris. Isr. J. Math. 194, 209–224 (2013). https://doi.org/10.1007/s11856-012-0071-7
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DOI: https://doi.org/10.1007/s11856-012-0071-7