{"paper":{"title":"On the number of real classes in the finite projective linear and unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"C. Ryan Vinroot, Elena Amparo","submitted_at":"2018-08-06T18:31:28Z","abstract_excerpt":"We show that for any $n$ and $q$, the number of real conjugacy classes in $\\mathrm{PGL}(n, \\mathbb{F}_q)$ is equal to the number of real conjugacy classes of $\\mathrm{GL}(n, \\mathbb{F}_q)$ which are contained in $\\mathrm{SL}(n, \\mathbb{F}_q)$, refining a result of Lehrer, and extending the result of Gill and Singh that this holds when $n$ is odd or $q$ is even. Further, we show that this quantity is equal to the number of real conjugacy classes in $\\mathrm{PGU}(n, \\mathbb{F}_q)$, and equal to the number of real conjugacy classes of $\\mathrm{U}(n, \\mathbb{F}_q)$ which are contained in $\\mathrm{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02058","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":""},"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"}