2025/11/19 by Fariña-Asategui, Jorge, Leemann, Paul-Henry, Nagnibeda, Tatiana
Mathematics · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Advanced Operator Algebra Research
paper · doi:10.48550/arxiv.2511.15277
For a weakly branch group G acting on a regular enough rooted tree, we provide two constructions of continuous families of distinct subgroups that are not closed in the profinite topology on G. On the one hand, we construct a continuous family of distinct non-closed subgroups such that each H in the family is not ERF, that is, contains subgroups not closed in the profinite topology on H. On the other hand, under an additional assumption on G, we construct a continuous family of ERF subgroups which are not closed in the congruence (and in the profinite) topology on G.