Subgroups of free-like pro-p groups and Hausdorff dimension

13 marzo 2019: Sala Seminario de Análisis, 18:00-19:00

Conferenciante: Oihana Garaialde Ocaña (Universidad del País Vasco)

Title: Subgroups of free-like pro-p groups and Hausdorff dimension

Abstract: Every finitely generated pro-p group G comes equipped with a metric space structure induced by a chosen filtration series. In this talk, we confine ourselves to the iterated p-power series, the Frattini series and the Zassenhaus series.

Given such a metric, the "size" of subgroups of G can be studied via their Hausdorff dimensions, a notion introduced in fractal geometry. The study of Hausdorff dimension in the context of pro-p (and more generally, profinite) groups was initiated more than twenty years ago by Barnea and Shalev. In this paper, the authors asked whether p-adic analytic pro-p groups can be distinguished or not via their Hausdorff spectra in the category of finitely generated pro-p groups.

After introducing the aforementioned notions and results, I will talk about the joint work with Benjamin Klopsch and Alejandra Garrido concerning the Hausdorff spectra of "free-like" pro-p groups.