{"paper":{"title":"On involutions and indicators of finite orthogonal groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.GR","authors_text":"C. Ryan Vinroot, Gregory K. Taylor","submitted_at":"2017-08-17T12:54:06Z","abstract_excerpt":"We study the numbers of involutions and their relation to Frobenius-Schur indicators in the groups $\\mathrm{SO}^{\\pm}(n,q)$ and $\\Omega^{\\pm}(n,q)$. Our point of view for this study comes from two motivations. The first is the conjecture that a finite simple group $G$ is strongly real (all elements are conjugate to their inverses by an involution) if and only if it is totally orthogonal (all Frobenius-Schur indicators are 1), and we are able to show this holds for all finite simple groups $G$ other than the groups $\\mathrm{Sp}(2n,q)$ with $q$ even or $\\Omega^{\\pm}(4m,q)$ with $q$ even. We prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05246","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"}