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19.10 (2018)

Open

a) Is it possible to embed a finitely generated non-abelian free pro-$p$ group as an open subgroup of a simple totally disconnected locally compact group?
b) If the answer is yes, can we require that the simple envelope is also compactly generated?

Contributor: Y. Barnea

Progress

*a) Yes, it is possible (Y. Barnea, M. Ershov, A. Le Boudec, C. D. Reid, M. Vannacci, T. Weigel, Preprint, 2025, https://arxiv.org/pdf/2507.04120).

Comment of 2025: Partial progress on part b) is made in (Y. Barnea, M. Ershov, A. Le Boudec, C. D. Reid, M. Vannacci, T. Weigel, Preprint, 2025, https://arxiv.org/pdf/2507.04120).

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