{"paper":{"title":"Center-freeness of finite-step solvable groups arising from anabelian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GR","authors_text":"Naganori Yamaguchi","submitted_at":"2026-01-12T00:36:11Z","abstract_excerpt":"Anabelian geometry suggests that, for suitably geometric objects, their \\'etale fundamental groups determine the geometric objects up to isomorphism. From a group-theoretic viewpoint, this philosophy requires rigidity properties, which often follow from their center-freeness of the associated \\'etale fundamental groups. In fact, some profinite groups arising from anabelian geometry are center-free. For any integer $m\\geq 2$, we investigate how such center-freeness behaves under passage to the maximal $m$-step solvable quotients. In particular, we show that the maximal $m$-step solvable quotien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.07112","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.07112/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}