Diffuse invariant random subgroups

Abstract

There exist countable groups G G with ergodic invariant random subgroups ν \nu such that ν ( { H ∈ S u b G ∣ H ≅ K } ) = 0 \nu (\, \{\, H \in \mathrm {Sub}_{G} \mid H \cong K \,\}\,) = 0 for every subgroup K ⩽ G K \leqslant G .