The lower $p$-series of analytic pro-$p$ groups and Hausdorff dimension
The lower $p$-series of analytic pro-$p$ groups and Hausdorff dimension
Let $G$ be a $p$-adic analytic pro-$p$ group of dimension $d$. We produce an approximate series which descends regularly in strata and whose terms deviate from the lower $p$-series in a uniformly bounded way. This brings to light a new set of rational invariants, canonically associated to $G$, that yield …