Solid Ergodicity and Orbit Equivalence Rigidity for Coinduced Actions

Abstract 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 $\Sigma <\Gamma $ are countable groups such $g\Sigma g^{-1}\cap \Sigma finite any $g\in \Gamma \setminus $. Then measure preserving action \curvearrowright X_0$ gives rise solidly ergodic equivalence relation if and only associated $\Gamma X$ ergodic. also obtain orbit rigidity actions by showing rigid or compact (T) group “remembered” X$.