A pro‐p group with full normal Hausdorff spectra

Iker de las Heras and Benjamin Klopsch

Mathematische Nachrichten, 2022, vol. 295, issue 1, 89-102

Abstract: For each odd prime p, we produce a 2‐generated pro‐p group G whose normal Hausdorff spectra hspec⊴S(G)=hdimGS(H)∣H⊴cG\begin{equation*}\hskip7pc \operatorname{hspec}_{\trianglelefteq }^{\mathcal {S}}(G) = {\left\lbrace \operatorname{hdim}_{G}^{\mathcal {S}}(H)\mid H\trianglelefteq _\mathrm{c} G \right\rbrace}\hskip-7pc \end{equation*}with respect to five standard filtration series S$\mathcal {S}$, namely the lower p‐series, the dimension subgroup series, the p‐power series, the iterated p‐power series and the Frattini series, are all equal to the full unit interval [0,1]. Here hdimGS:{X∣X⊆G}→[0,1]$\operatorname{hdim}_G^{\mathcal {S}} : \lbrace X\mid X \subseteq G \rbrace \rightarrow [0,1]$ denotes the Hausdorff dimension function associated to the natural translation‐invariant metric induced by the filtration series S$\mathcal {S}$.

Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202000164

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:295:y:2022:i:1:p:89-102

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().