{"paper":{"title":"Strongly real classes in finite unitary groups of odd characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Anupam Singh, C. Ryan Vinroot, Zachary Gates","submitted_at":"2013-03-25T11:07:24Z","abstract_excerpt":"We classify all strongly real conjugacy classes of the finite unitary group $\\U(n, F_q)$ when $q$ is odd. In particular, we show that $g \\in \\U(n, F_q)$ is strongly real if and only if $g$ is an element of some embedded orthogonal group $O^{\\pm}(n, F_q)$. Equivalently, $g$ is strongly real in $\\U(n, F_q)$ if and only if $g$ is real and every elementary divisor of $g$ of the form $(t \\pm 1)^{2m}$ has even multiplicity. We apply this to obtain partial results on strongly real classes in the finite symplectic group $\\Sp(2n, F_q)$, $q$ odd, and a generating function for the number of strongly real"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6085","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"}