A pro-p group with infinite normal Hausdorff spectra
(2019) In Pacific Journal of Mathematics 303(2). p.569-603- Abstract
- Using wreath products, we construct a finitely generated pro-p group G with infinite normal Hausdorff spectrum here hdim p G : (X|X ⊂ G) [0,1]denotes the Hausdorff dimension function associated to the p-power series p:Gpi, i ε N0 More precisely, we show that hspec p (G)=[0,1/3] ∪ (1) contains an infinite interval; this settles a question of Shalev. Furthermore, we prove that the normal Hausdorff spectra hspec (G) with respect to other filtration series S have a similar shape. In particular, our analysis applies to standard filtration series such as the Frattini series, the lower p-series and the modular dimension subgroup series. Lastly, we pin down the ordinary Hausdorff spectra with respect to the standard filtration series S. The... (More)
- Using wreath products, we construct a finitely generated pro-p group G with infinite normal Hausdorff spectrum here hdim p G : (X|X ⊂ G) [0,1]denotes the Hausdorff dimension function associated to the p-power series p:Gpi, i ε N0 More precisely, we show that hspec p (G)=[0,1/3] ∪ (1) contains an infinite interval; this settles a question of Shalev. Furthermore, we prove that the normal Hausdorff spectra hspec (G) with respect to other filtration series S have a similar shape. In particular, our analysis applies to standard filtration series such as the Frattini series, the lower p-series and the modular dimension subgroup series. Lastly, we pin down the ordinary Hausdorff spectra with respect to the standard filtration series S. The spectrum hspecL.(G) for the lower p-series L displays surprising new features. © 2019 Mathematical Sciences Publishers. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/b3028d3a-7944-4d72-a68d-2150c83bf619
- author
- Klopsch, Benjamin and Thillaisundaram, Anitha LU
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Pacific Journal of Mathematics
- volume
- 303
- issue
- 2
- pages
- 569 - 603
- publisher
- Pacific Journal of Mathematics
- external identifiers
-
- scopus:85079270148
- ISSN
- 0030-8730
- DOI
- 10.2140/pjm.2019.303.569
- language
- English
- LU publication?
- no
- id
- b3028d3a-7944-4d72-a68d-2150c83bf619
- date added to LUP
- 2024-06-07 14:26:13
- date last changed
- 2024-08-07 10:28:21
@article{b3028d3a-7944-4d72-a68d-2150c83bf619,
abstract = {{Using wreath products, we construct a finitely generated pro-p group G with infinite normal Hausdorff spectrum here hdim p G : (X|X ⊂ G) [0,1]denotes the Hausdorff dimension function associated to the p-power series p:Gpi, i ε N0 More precisely, we show that hspec p (G)=[0,1/3] ∪ (1) contains an infinite interval; this settles a question of Shalev. Furthermore, we prove that the normal Hausdorff spectra hspec (G) with respect to other filtration series S have a similar shape. In particular, our analysis applies to standard filtration series such as the Frattini series, the lower p-series and the modular dimension subgroup series. Lastly, we pin down the ordinary Hausdorff spectra with respect to the standard filtration series S. The spectrum hspecL.(G) for the lower p-series L displays surprising new features. © 2019 Mathematical Sciences Publishers.}},
author = {{Klopsch, Benjamin and Thillaisundaram, Anitha}},
issn = {{0030-8730}},
language = {{eng}},
number = {{2}},
pages = {{569--603}},
publisher = {{Pacific Journal of Mathematics}},
series = {{Pacific Journal of Mathematics}},
title = {{A pro-p group with infinite normal Hausdorff spectra}},
url = {{http://dx.doi.org/10.2140/pjm.2019.303.569}},
doi = {{10.2140/pjm.2019.303.569}},
volume = {{303}},
year = {{2019}},
}