Klopsch, Benjamin and Thillaisundaram, Anitha (2020) A prop group with infinite normal Hausdorff spectra. Pacific Journal of Mathematics . ISSN UNSPECIFIED
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Item Type:  Article 

Item Status:  Live Archive 
Abstract
Using wreath products, we construct a finitely generated prop group G with infinite normal Hausdorff spectrum with respect to the ppower 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 pseries 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 pseries displays surprising new features.
Keywords:  prop 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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