On a co-induction question of Kechris

Abstract

This note answers a question of Kechris: if $H<G$ is a normal subgroup of a countable group $G$, $H$ has property MD and $G/H$ is amenable and residually finite then $G$ also has property MD. Under the same hypothesis we prove that for any action $a$ of $G$, if $b$ is a free action of $G/H$, and $b_G$ is the induced action of $G$ then $\CInd_H^G(a|H) \times b_G$ weakly contains $a$. Moreover, if $H<G$ is any subgroup of a countable group $G$, and the action of $G$ on $G/H$ is amenable, then $\CInd_H^G(a|H)$ weakly contains $a$ whenever $a$ is a Gaussian action.

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References in corpus (1)

• Orbit inequivalent actions for groups containing a copy of ${\mathbb{F}}_2$