Factor orbit equivalence of compact group extensions and classification of finite extensions of ergodic automorphisms

In §§1–5, we classifyn-point extensions of ergodic automorphisms up to factor orbit-equivalence (which is the natural analogue of factor isomorphism). This classification is in terms of conjugacy classes of subgroups of the symmetric group onn points, and parallels D. Rudolph’s classification ofn-point extensions of Bernoulli shifts up to factor isomorphism. In §6, we give another proof of A. Fieldsteel’s theorem on factor orbit-equivalence of compact group extensions.