Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

A pro-2 group with full normal Hausdorff spectra

De Las Heras, Iker and Thillaisundaram, Anitha LU (2022) In Journal of Group Theory
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.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
epub
subject
in
Journal of Group Theory
publisher
De Gruyter
external identifiers
  • scopus:85126543053
ISSN
1433-5883
DOI
10.1515/jgth-2021-0017
language
English
LU publication?
yes
id
0017ff2c-ad8f-4f0e-ad1e-5515230213ad
date added to LUP
2022-05-02 16:06:39
date last changed
2022-05-02 16:06:39
@article{0017ff2c-ad8f-4f0e-ad1e-5515230213ad,
  abstract     = {{<p>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. </p>}},
  author       = {{De Las Heras, Iker and Thillaisundaram, Anitha}},
  issn         = {{1433-5883}},
  language     = {{eng}},
  publisher    = {{De Gruyter}},
  series       = {{Journal of Group Theory}},
  title        = {{A pro-2 group with full normal Hausdorff spectra}},
  url          = {{http://dx.doi.org/10.1515/jgth-2021-0017}},
  doi          = {{10.1515/jgth-2021-0017}},
  year         = {{2022}},
}