A pro-2 group with full normal Hausdorff spectra-Reference-Cited by-同舟云学术

A pro-2 group with full normal Hausdorff spectra

Published:2022-03-03 Issue:0 Volume:0 Page:
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

de las Heras Iker¹^ORCID,Thillaisundaram Anitha²

Affiliation:

1. Mathematisches Institut , Heinrich-Heine-Universität , 40225 Düsseldorf , Germany ; and Department of Mathematics, University of the Basque Country UPV/EHU, 48940 Leioa, Spain

2. Centre for Mathematical Sciences , Lund University , 223 62 Lund , Sweden

Abstract

Abstract We construct a 2-generated pro-2 group with full normal Hausdorff spectrum [ 0 , 1 ]

[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.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2021-0017/pdf

Reference9 articles.

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3. I. de las Heras and B. Klopsch, A pro-𝑝 group with full normal Hausdorff spectra, Math. Nachr., to appear.

4. J. D. Dixon, M. P. F. du Sautoy, A. Mann and D. Segal, Analytic pro-𝑝 Groups, 2nd ed., Cambridge Stud. Adv. Math. 61, Cambridge University, Cambridge, 1999.

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