Admissible subgroups of full ergodic groups
1996 ◽
Vol 16
(6)
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pp. 1221-1239
Keyword(s):
Type Ii
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AbstractLet 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].
1989 ◽
Vol 40
(1)
◽
pp. 109-111
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Keyword(s):
1981 ◽
Vol 33
(2)
◽
pp. 412-420
◽
Keyword(s):
Keyword(s):
2005 ◽
Vol 04
(02)
◽
pp. 165-171
Keyword(s):
2011 ◽
Vol 168
(1)
◽
pp. 113-124
◽
2015 ◽
Vol 43
(11)
◽
pp. 4797-4808
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Keyword(s):