A pro-p group with infinite normal Hausdorff spectra

Klopsch, Benjamin and Thillaisundaram, Anitha (2019) A pro-p group with infinite normal Hausdorff spectra. Pacific Journal of Mathematics, 303 (2). pp. 569-603. ISSN 0030-8730

Full content URL: https://doi.org/10.2140/pjm.2019.303.569

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A pro-p group with infinite normal Hausdorff spectra
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Abstract

Using wreath products, we construct a finitely generated pro-p group G with infinite normal Hausdorff spectrum with respect to the p-power series. More precisely, we show that this normal Hausdorff spectrum contains an infinite interval; this settles a question of Shalev. Furthermore, we prove that the normal Hausdorff spectra of G with respect to other filtration series 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 of G with respect to the standard filtration series. The spectrum of G for the lower p-series displays surprising new features.

Keywords:pro-p groups, Hausdorff dimension, Hausdorff spectrum, normal Hausdorff spectrum
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:36794
Deposited On:28 Aug 2019 08:40

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