On the Hausdorff spectra of free pro-$p$ groups and certain $p$-adic analytic groups

Iker de las Heras, Benjamin Klopsch, Anitha Thillaisundaram

We establish that finitely generated non-abelian direct products $G$ of free pro-$p$ groups have full Hausdorff spectrum with respect to the lower $p$-series $\mathcal{L}$. This co…