A pro-2 group with full normal Hausdorff spectra

2021/02/03 by Iker de las Heras, Heras, Iker de las, Anitha Thillaisundaram +1 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Mathematical Dynamics and Fractals #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2102.02117

Abstract

We construct a 2-generated pro-2 group with full normal Hausdorff spectrum [0,1], with respect to each of the four standard filtration series: the 2-power series, the lower 2-series, the Frattini series, and the dimension subgroup series. This answers a question of Klopsch and the second author, for the even prime case; the odd prime case was settled by the first author and Klopsch. Also, our construction gives the first example of a finitely generated pro-2 group with full Hausdorff spectrum with respect to the lower 2-series.

Cited by

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

Related

• The finitely generated Hausdorff spectra of a family of pro-p groups
• A pro-p group with full normal Hausdorff spectra
• Normal Hausdorff spectra of pro-2 groups
• The lower p-series of analytic pro-p groups and Hausdorff dimension
• Hausdorff dimensions in p-adic analytic groups