## 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 W_{1} and H_{2} of [G], the following problem is considered: when are the full subgroups [H_{1}] and [H_{2}] 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 [H_{0}] of [G] and a countable subgroup Γ ⊂ N[H_{0}] consisting of automorphisms which are outer for [H_{0}], such that [H_{0}] ⊂ [H] ⊂ [G] and the full subgroup [H_{0}, Γ] generated by [H_{0}] and Γ coincides with [G].

Original language | English |
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Pages (from-to) | 1221-1239 |

Number of pages | 19 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 16 |

Issue number | 6 |

DOIs | |

State | Published - 1 Jan 1996 |

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics