The finitely generated Hausdorff spectra of a family of pro-p groups
(2022) In Journal of Algebra 606. p.266-297- Abstract
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 p-adic 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.
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https://lup.lub.lu.se/record/1366571a-b005-4038-9cfb-040e75f9527a
- author
- de las Heras, Iker and Thillaisundaram, Anitha LU
- organization
- publishing date
- 2022-09-15
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Finitely generated Hausdorff spectrum, Hausdorff dimension, Normal Hausdorff spectrum, Pro-p groups
- in
- Journal of Algebra
- volume
- 606
- pages
- 32 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85130550469
- ISSN
- 0021-8693
- DOI
- 10.1016/j.jalgebra.2022.05.008
- language
- English
- LU publication?
- yes
- id
- 1366571a-b005-4038-9cfb-040e75f9527a
- date added to LUP
- 2022-12-27 15:08:02
- date last changed
- 2022-12-27 15:08:02
@article{1366571a-b005-4038-9cfb-040e75f9527a, abstract = {{<p>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 p-adic 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.</p>}}, author = {{de las Heras, Iker and Thillaisundaram, Anitha}}, issn = {{0021-8693}}, keywords = {{Finitely generated Hausdorff spectrum; Hausdorff dimension; Normal Hausdorff spectrum; Pro-p groups}}, language = {{eng}}, month = {{09}}, pages = {{266--297}}, publisher = {{Elsevier}}, series = {{Journal of Algebra}}, title = {{The finitely generated Hausdorff spectra of a family of pro-p groups}}, url = {{http://dx.doi.org/10.1016/j.jalgebra.2022.05.008}}, doi = {{10.1016/j.jalgebra.2022.05.008}}, volume = {{606}}, year = {{2022}}, }