{"paper":{"title":"$\\theta$-semisimple twisted conjugacy classes of type D in $\\operatorname{PSL}_n(q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.QA","authors_text":"Agust\\'in Garc\\'ia Iglesias, Giovanna Carnovale","submitted_at":"2015-01-30T00:28:07Z","abstract_excerpt":"Let $p$ be an odd prime, $m\\in {\\mathbb N}$ and set $q=p^m$, $G=\\operatorname{PSL}_n(q)$. Let $\\theta$ be a standard graph automorphism of $G$, $d$ be a diagonal automorphism and $\\operatorname{Fr}_q$ be the Frobenius endomorphism of $\\operatorname{PSL}_n(\\overline{{\\mathbb F}_q})$. We show that every $(d\\circ \\theta)$-conjugacy class of a $(d\\circ \\theta,p)$-regular element in $G$ is represented in some $\\operatorname{Fr}_q$-stable maximal torus and that most of them are of type D. We write out the possible exceptions and show that, in particular, if $n\\geq5$ is either odd or a multiple of $4"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07638","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":""},"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"}