Speedups of ergodic group extensions

Abstract: We prove that for all ergodic extensions S-1 of a transformation by a locally compact second countable group G, and for all G-extensions S₂ of an aperiodic transformation, there is a relative speedup of S₁ that is relatively isomorphic to S₂. We apply this result to give necessary and sufficient conditions for two ergodic n-point or countable extensions to be related in this way.Keywords: Classification, Factor orbit equivalence, Compact group extension