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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.