{"paper":{"title":"The binary actions of simple groups of Lie type of characteristic 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Martin W. Liebeck, Nick Gill, Pierre Guillot","submitted_at":"2024-02-13T10:37:17Z","abstract_excerpt":"Let $\\mathcal{C}$ be a conjugacy class of involutions in a group $G$. We study the graph $\\Gamma(\\mathcal{C})$ whose vertices are elements of $\\mathcal{C}$ with $g,h\\in\\mathcal{C}$ connected by an edge if and only if $gh\\in\\mathcal{C}$. For $t\\in \\mathcal{C}$, we define the component group of $t$ to be the subgroup of $G$ generated by all vertices in $\\Gamma(\\mathcal{C})$ that lie in the connected component of the graph that contains $t$.\n  We classify the component groups of all involutions in simple groups of Lie type over a field of characteristic $2$. We use this classification to partiall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.08357","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/2402.08357/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"}