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arXiv · 2511.15277

Non-closed subgroups of weakly branch groups

Jorge Fariña-Asategui·Paul-Henry Leemann·Tatiana Nagnibeda
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Abstract

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 $G$.

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Jorge Fariña-Asategui, Paul-Henry Leemann, Tatiana Nagnibeda. 2025-11-19. Non-closed subgroups of weakly branch groups. https://arxiv.org/abs/2511.15277

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