Logic Seminar

Let F be a nonabelian free group. We show that, for any two nontrivial finite groups, the natural actions of the wreath product groups A≀F and B≀F, on AF and BF respectively, are orbit equivalent. On the other hand, we show that these actions are not even stably orbit equivalent if F is replaced with any ICC sofic group with property (T), and A and B have different cardinalities. This is joint work with Konrad Wrobel.