2021/06/24 by Iker de las Heras, Heras, Iker de las, Anitha Thillaisundaram +1
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2106.12972
openalex publication_date 2021/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently the first example of a family of pro-p groups, for p a prime, with full normal Hausdorff spectrum was constructed. In this paper we further investigate this family by computing their finitely generated Hausdorff spectrum with respect to each of the five standard filtration series: the p-power series, the iterated p-power series, the lower p-series, the Frattini series and the dimension subgroup series. Here the finitely generated Hausdorff spectra of these groups consist of infinitely many rational numbers, and their computation requires a rather technical approach. This result also gives further evidence to the non-existence of a finitely generated pro-p group with uncountable finitely generated Hausdorff spectrum.