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 , 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 .
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
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