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

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

2007-03-24

arxiv.org/abs/math/0703726v1

Mathematics

Group Theory

Scientific paper

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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