{"paper":{"title":"Generation of finite classical groups by pairs of elements with large fixed point spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"\\'Akos Seress, Cheryl E. Praeger, \\c{S}\\\"ukr\\\"u Yal\\c{c}inkaya","submitted_at":"2014-03-09T13:46:12Z","abstract_excerpt":"We study `good elements' in finite $2n$-dimensional classical groups $G$: namely $t$ is a `good element' if $o(t)$ is divisible by a primitive prime divisor of $q^n-1$ for the relevant field order $q$, and $t$ fixes pointwise an $n$-space. The group ${\\rm{SL}}_{2n}(q)$ contains such elements, and they are present in ${\\rm{Su}}_{2n}(q), {\\rm{Sp}}_{2n}(q), {\\rm{So}}^\\epsilon_{2n}(q)$, only if $n$ is odd, even, even, respectively. We prove that there is an absolute positive constant $c$ such that two random conjugates of $t$ generate $G$ with probability at least $c$, if $G\\ne {\\rm{Sp}}_{2n}(q)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2057","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"}