Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

The finitely generated Hausdorff spectra of a family of pro-p groups

de las Heras, Iker and Thillaisundaram, Anitha LU (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.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
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}},
}