{"paper":{"title":"Conjugacy in finite classical groups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"E.A. O'Brien, Giovanni De Franceschi, Martin W. Liebeck","submitted_at":"2024-01-15T09:44:29Z","abstract_excerpt":"Let $G$ be a classical group defined over a finite field. We consider the following fundamental problems concerning conjugacy in $G$:\n  1. List a representative for each conjugacy class of $G$.\n  2. Given $x \\in G$, describe the centralizer of $x$ in $G$, by giving its group structure and a generating set.\n  3. Given $x,y \\in G$, establish whether $x$ and $y$ are conjugate in $G$ and, if so, then find explicit $z \\in G$ such that $z^{-1}xz = y$.\n  We present comprehensive theoretical solutions to all three problems, and use our solutions to formulate practical algorithms. In parallel to our th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.07557","kind":"arxiv","version":2},"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/2401.07557/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"}