The lower pp‐series of analytic pro‐pp groups and Hausdorff dimension

Key Points

• The Hausdorff dimensions of closed subgroups are limited to a discrete set of rational numbers, suggesting a rich structure for analytic pro-p groups.
• An approximate series is developed that descends in strata, with deviations from the lower p-series remaining uniformly bounded.
• This work introduces rational invariants that are canonically linked to analytic pro-p groups and their structural dimensions.
• The findings imply that closed subgroups exhibit a distinct Hausdorff spectrum, reinforcing the complex interplay of dimensions in pro-p groups.