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Admissible subgroups of full ergodic groups

Published online by Cambridge University Press:  14 October 2010

Andrey Fedorov  and
Ben-Zion Rubshtein
Andrey Fedorov
Affiliation:
Astrakhan State Pedogogic Institute, Astrakhan, Russia
Ben-Zion Rubshtein
Affiliation:
Ben-Gurion University of the Negev, Beer-Sheva, Israel
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Abstract

Let G be a countable group of automorphisms of a Lebesgue space (X, m) and let [G] be the full group of G. For a pair of countable ergodic subgroups H1 and H2 of [G], the following problem is considered: when are the full subgroups [H1] and [H2] conjugate in the normalizer N[G] = {g ∈ Aut X: g[G]g-1 = [G]} of [G]. A complete solution of the problem is given in the case when [G] is an approximately finite group of type II and [H] is admissible, in the sense that there exists an ergodic subgroup [H0] of [G] and a countable subgroup Γ ⊂ N[H0] consisting of automorphisms which are outer for [H0], such that [H0] ⊂ [G] and the full subgroup [Ho, Γ] generated by [H0] and Γ coincides with [G].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 6 , December 1996 , pp. 1221 - 1239
Copyright
Copyright © Cambridge University Press 1996

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