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This article is cited in 29 scientific papers (total in 30 papers)
Totally nonfree actions and the infinite symmetric group
A. M. Vershikab
a St. Petersburg Department of Steklov Institute of Mathematics
b Max Planck Institute, Bonn
Abstract:
We consider totally nonfree (TNF) actions of groups and the corresponding adjoint invariant (AD) measures on lattices of the subgroups of the given group. The main result is the description of all adjoint-invariant and TNF measures on the lattice of subgroups of the infinite symmetric group $S_\mathbb N$. The problem is closely related to the theory of characters and factor representations of groups.
Key words and phrases:
totally nonfree actions, infinite symmetric group, random subgroups.
DOI:
https://doi.org/10.17323/1609-4514-2012-12-1-193-212
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http://www.ams.org/.../abst12-1-2012.html
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MSC: 37A15, 20B35, 22D40
Received: October 4, 2011
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Citation:
A. M. Vershik, “Totally nonfree actions and the infinite symmetric group”, Mosc. Math. J., 12:1 (2012), 193–212
Citation in format AMSBIB
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\by A.~M.~Vershik
\paper Totally nonfree actions and the infinite symmetric group
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 1
\pages 193--212
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http://mi.mathnet.ru/eng/mmj453 http://mi.mathnet.ru/eng/mmj/v12/i1/p193
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   -
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 -
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-
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-
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-
Dudko A., Medynets K., “Finite Factor Representations of Higman-Thompson Groups”, Group. Geom. Dyn., 8:2 (2014), 375–389
-
Yu. A. Neretin, “Infinite symmetric groups and combinatorial constructions of topological field theory type”, Russian Math. Surveys, 70:4 (2015), 715–773
-
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-
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-
D'Angeli D., Rodaro E., “a Geometric Approach To (Semi)-Groups Defined By Automata Via Dual Transducers”, Geod. Dedic., 174:1 (2015), 375–400
-
Cannizzo J., “the Boundary Action of a Sofic Random Subgroup of the Free Group”, Group. Geom. Dyn., 9:3 (2015), 683–709
-
Bowen L., “Invariant Random Subgroups of the Free Group”, Group. Geom. Dyn., 9:3 (2015), 891–916
-
Glasner E., Weiss B., “Uniformly Recurrent Subgroups”, Recent Trends in Ergodic Theory and Dynamical Systems, Contemporary Mathematics, 631, eds. Bhattacharya S., Das T., Ghosh A., Shah R., Amer Mathematical Soc, 2015, 63–75
-
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-
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-
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-
I. Biringer, O. Tamuz, “Unimodularity of invariant random subgroups”, Trans. Am. Math. Soc., 369:6 (2017), 4043–4061
-
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-
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-
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-
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-
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-
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-
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-
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