{"paper":{"title":"Hausdorff dimensions in $p$-adic analytic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Amaia Zugadi-Reizabal, Anitha Thillaisundaram, Benjamin Klopsch","submitted_at":"2017-02-22T13:18:24Z","abstract_excerpt":"Let $G$ be a finitely generated pro-$p$ group, equipped with the $p$-power series. The associated metric and Hausdorff dimension function give rise to the Hausdorff spectrum, which consists of the Hausdorff dimensions of closed subgroups of $G$. In the case where $G$ is $p$-adic analytic, the Hausdorff dimension function is well understood; in particular, the Hausdorff spectrum consists of finitely many rational numbers closely linked to the analytic dimensions of subgroups of $G$.\n  Conversely, it is a long-standing open question whether the finiteness of the Hausdorff spectrum implies that $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06789","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}