Solid Ergodicity and Orbit Equivalence Rigidity for Coinduced Actions

We prove that the solid ergodicity property is stable with respect to taking coinduction for a fairly large class of coinduced action. More precisely, assume that Sigma < Gamma are countable groups such that g Sigma g(-1) boolean AND Sigma is finite for any g is an element of Gamma \ Sigma . Then any measure preserving action Sigma boolean AND X-0 gives rise to a solidly ergodic equivalence relation if and only if the equivalence relation of the associated coinduced action Gamma boolean AND X is solidly ergodic. We also obtain orbit equivalence rigidity for such actions by showing that the orbit equivalence relation of a rigid or compact measure preserving action Sigma boolean AND X-0 of a property (T) group is "remembered" by the orbit equivalence relation of Gamma boolean AND X.