{"paper":{"title":"On the second-largest Sylow subgroup of a finite simple group of Lie type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alice C. Niemeyer, S.P. Glasby, Tomasz Popiel","submitted_at":"2017-12-16T03:53:59Z","abstract_excerpt":"Let $T$ be a finite simple group of Lie type in characteristic $p$, and let $S$ be a Sylow subgroup of $T$ with maximal order. It is well known that $S$ is a Sylow $p$-subgroup except in an explicit list of exceptions, and that $S$ is always `large' in the sense that $|T|^{1/3} < |S| \\leqslant |T|^{1/2}$. One might anticipate that, moreover, the Sylow $r$-subgroups of $T$ with $r \\neq p$ are usually significantly smaller than $S$. We verify this hypothesis by proving that for every $T$ and every prime divisor $r$ of $|T|$ with $r \\neq p$, the order of the Sylow $r$-subgroup of $T$ at most $|T|"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05899","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"}