English

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

Group Theory 2007-05-23 v1 Logic

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.

Keywords

Cite

@article{arxiv.math/0703726,
  title  = {Less than continuum many translates of a compact nullset may cover any infinite profinite group},
  author = {Miklos Abert},
  journal= {arXiv preprint arXiv:math/0703726},
  year   = {2007}
}