English

Hausdorff dimension of closed subsets in profinite groups

Group Theory 2021-01-26 v2

Abstract

A countably based profinite group can be naturally seen as a metric space with respect to a given filtration, and thus, it has a well defined Hausdorff dimension function. Barnea and Shalev found a group theoretical expression for the Hausdorff dimension of the closed subgroups of a profinite group GG, opening, in this way, a bunch of possibilities to explore. In this paper we generalize Barnea's and Shalev's result to arbitrary closed subsets of GG.

Keywords

Cite

@article{arxiv.2004.14210,
  title  = {Hausdorff dimension of closed subsets in profinite groups},
  author = {Iker de las Heras},
  journal= {arXiv preprint arXiv:2004.14210},
  year   = {2021}
}

Comments

There is an error on Line -6 of Page 6

R2 v1 2026-06-23T15:11:05.327Z