Coverings and dimensions in infinite profinite groups

• Autorzy: Peter Maga
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Profinite group; Box dimension; Hausdorff dimension; Cover; Continuum; Consistent

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 22C05: Compact groups
• 03E35: Consistency and independence results

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 2
• Strony: 246-253

Daty

wydano

2013-02-01

online

2012-11-21

Twórcy

autor

Peter Maga

• Central European University

Bibliografia

• [1] Abért M., Less than continuum many translates of a compact nullset may cover any infinite profinite group, J. Group Theory, 2008, 11(4), 545–553 http://dx.doi.org/10.1515/JGT.2008.033
• [2] Barnea Y., Shalev A., Hausdorff dimension, pro-p groups and Kac-Moody algebras, Trans. Amer. Math. Soc., 1997, 349(12), 5073–5091 http://dx.doi.org/10.1090/S0002-9947-97-01918-1
• [3] Bartoszynski T., Judah H., Set Theory, A.K.Peters, Wellesley, 1995
• [4] Darji U.B., Keleti T., Covering ℝ with translates of a compact set, Proc. Amer. Math. Soc., 2003, 131(8), 2593–2596 http://dx.doi.org/10.1090/S0002-9939-02-06773-4
• [5] Elekes M., Steprāns J., Less than 2ω many translates of a compact nullset may cover the real line, Fund. Math., 2004, 181(1), 89–96 http://dx.doi.org/10.4064/fm181-1-4
• [6] Elekes M., Tóth Á., Covering locally compact groups by less than 2ω many translates of a compact nullset, Fund. Math., 2007, 193(3), 243–257 http://dx.doi.org/10.4064/fm193-3-2
• [7] Gruenhage G., Levy R., Covering ωω by special Cantor sets, Comment. Math. Univ. Carolin., 2002, 43(3), 497–509
• [8] Máthé A., Covering the real line with translates of a zero-dimensional compact set, Fund. Math., 2011, 213(3), 213–219 http://dx.doi.org/10.4064/fm213-3-2

Identyfikatory

DOI

10.2478/s11533-012-0113-8