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arXiv · 2102.02117

A pro-2 group with full normal Hausdorff spectra

Iker de las Heras·Anitha Thillaisundaram
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Abstract

We construct a $2$-generated pro-$2$ group with full normal Hausdorff spectrum $[0,1]$, with respect to each of the four standard filtration series: the $2$-power series, the lower $2$-series, the Frattini series, and the dimension subgroup series. This answers a question of Klopsch and the second author, for the even prime case; the odd prime case was settled by the first author and Klopsch. Also, our construction gives the first example of a finitely generated pro-$2$ group with full Hausdorff spectrum with respect to the lower $2$-series.

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Iker de las Heras, Anitha Thillaisundaram. 2021-02-03. A pro-2 group with full normal Hausdorff spectra. https://arxiv.org/abs/2102.02117

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