The lower p-series of analytic pro-p groups and Hausdorff dimension

2024/02/10 by Iker de las Heras, Heras, Iker de las, Benjamin Klopsch +3 · 1 citation
Decision Sciences · Mathematics · #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2402.06876

openalex publication_date 2024/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let G be a p-adic analytic pro-p group of dimension d. We produce an approximate series which descends regularly in strata and whose terms deviate from the lower p-series in a uniformly bounded way. This brings to light a new set of rational invariants, canonically associated to G, that yield the aforementioned uniform bound and that restrict the possible values for the Hausdorff dimensions of closed subgroups of G with respect to the lower p-series. In particular, the Hausdorff spectrum of G with respect to the lower p-series is discrete and consists of at most 2^d rational numbers.

Cited by

• On the Hausdorff spectra of free pro-p groups and certain p-adic analytic groups

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