Admissible subgroups of full ergodic groups

Andrey Fedorov, Ben Zion Rubshtein

Research output: Contribution to journalArticlepeer-review


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 W1 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] ⊂ [H] ⊂ [G] and the full subgroup [H0, Γ] generated by [H0] and Γ coincides with [G].

Original languageEnglish
Pages (from-to)1221-1239
Number of pages19
JournalErgodic Theory and Dynamical Systems
Issue number6
StatePublished - 1 Jan 1996

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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