# Coverings and dimensions in infinite profinite groups

Open Mathematics (2013)

- Volume: 11, Issue: 2, page 246-253
- ISSN: 2391-5455

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topPeter Maga. "Coverings and dimensions in infinite profinite groups." Open Mathematics 11.2 (2013): 246-253. <http://eudml.org/doc/269434>.

@article{PeterMaga2013,

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.},

author = {Peter Maga},

journal = {Open Mathematics},

keywords = {Profinite group; Box dimension; Hausdorff dimension; Cover; Continuum; Consistent; profinite group; box dimension; cover; continuum; consistent},

language = {eng},

number = {2},

pages = {246-253},

title = {Coverings and dimensions in infinite profinite groups},

url = {http://eudml.org/doc/269434},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Peter Maga

TI - Coverings and dimensions in infinite profinite groups

JO - Open Mathematics

PY - 2013

VL - 11

IS - 2

SP - 246

EP - 253

AB - 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.

LA - eng

KW - Profinite group; Box dimension; Hausdorff dimension; Cover; Continuum; Consistent; profinite group; box dimension; cover; continuum; consistent

UR - http://eudml.org/doc/269434

ER -

## References

top- [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 Zbl1146.22002
- [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 Zbl0892.20020
- [3] Bartoszynski T., Judah H., Set Theory, A.K.Peters, Wellesley, 1995
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- [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 Zbl1095.28005
- [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 Zbl1120.22002
- [7] Gruenhage G., Levy R., Covering ωω by special Cantor sets, Comment. Math. Univ. Carolin., 2002, 43(3), 497–509 Zbl1072.03028
- [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 Zbl1230.03079

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