{"paper":{"title":"Element order versus minimal degree in permutation groups: an old lemma with new applications","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"\\'Akos Seress, L\\'aszl\\'o Babai","submitted_at":"2014-01-02T18:07:54Z","abstract_excerpt":"In this note we present a simplified and slightly generalized version of a lemma the authors published in 1987. The lemma as stated here asserts that if the order of a permutation of $n$ elements is greater than $n^{\\alpha}$ then some non-identity power of the permutation has support size less than $n/{\\alpha}$. The original version made an unnecessary additional assumption on the cycle structure of the permutation; the proof of the present cleaner version follows the original proof verbatim. Application areas include parallel and sequential algorithms for permutation groups, the diameter of C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0489","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"}