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Less than continuum many translates of a compact nullset may cover any infinite profinite group

Miklos Abert
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Abstract

We show that it is consistent with the axioms of set theory that every infinite profinite group G possesses a closed subset X of Haar measure zero such that less than continuum many translates of X cover G. This answers a question of Elekes and Toth and by their work settles the problem for all infinite compact topological groups.

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Miklos Abert. 2007-03-24. Less than continuum many translates of a compact nullset may cover any infinite profinite group. https://arxiv.org/abs/math/0703726

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