Randomizations of groups are connected

Itaï Ben Yaacov (1) , Jorge Muñoz Carvajal (1)

1 AGL - Algèbre, géométrie, logique

Randomizations are continuous structures consisting of random variables with values on a given family of structures. We show that if G is a definable group on a continuous structure then G^R , the randomization of the group, defined as the set of variables whose values belong to the group, is definably connected, i.e. it has no proper invariant subgroups of bounded index.

Domaines: Logique [math.LO]

Itaï Ben Yaacov, Jorge Muñoz Carvajal. Randomizations of groups are connected. 2021. ⟨hal-03187898v2⟩