Measure space automorphisms, the normalizers of their full groups, and approximate finiteness - Connes, Alain; Krieger, Wolfgang (Journal of functional analysis, 2004)
We deal with the normalizer N[T] of the full group [T] of a nonsingular transformation T of a Lebesgue measure space in the group of all nonsingular transformations. We solve the conjugacy problem in N[T]/[T] for a measure preserving and ergodic T. Our results show that a locally finite extension of a solvable group is approximately finite.