Abstract
Answering a question of Miklós Abért, we prove that an infinite profinite group cannot be the union of less than continuum many translates of a compact subset of box dimension less than 1. Furthermore, we show that it is consistent with the axioms of set theory that in any infinite profinite group there exists a compact subset of Hausdorff dimension 0 such that one can cover the group by less than continuum many translates of it.
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Maga, P. Coverings and dimensions in infinite profinite groups. centr.eur.j.math. 11, 246–253 (2013). https://doi.org/10.2478/s11533-012-0113-8
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DOI: https://doi.org/10.2478/s11533-012-0113-8