{"paper":{"title":"Computing canonical labellings of finite solvable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Heiko Dietrich, Max Horn, Santiago Barrera Acevedo","submitted_at":"2026-06-24T17:02:33Z","abstract_excerpt":"We define a canonical labelling function on the class of finite solvable groups so that two such groups $G$ and $H$ are isomorphic if and only if can$(G)=$can$(H)$. Specifically, can$(G)$ is a group presentation that describes a group isomorphic to $G$, and our description explains how to construct an isomorphism $G\\to$can$(G)$. Our approach is motivated by O'Brien's (1993) canonical presentations for finite $p$-groups and utilises ideas from group cohomology first described by Robinson (1982) and automorphism group algorithms developed by Smith (1994), Holt (2001), and others. We also discuss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26030","kind":"arxiv","version":1},"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/2606.26030/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"}