{"paper":{"title":"Identifying long cycles in finite alternating and symmetric groups acting on subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.GR","authors_text":"Alice C. Niemeyer, Cheryl E. Praeger, Steve Linton","submitted_at":"2012-05-30T08:48:56Z","abstract_excerpt":"Let $H$ be a permutation group on a set $\\Lambda$, which is permutationally isomorphic to a finite alternating or symmetric group $A_n$ or $S_n$ acting on the $k$-element subsets of points from $\\{1,\\ldots,n\\}$, for some arbitrary but fixed $k$. Suppose moreover that no isomorphism with this action is known. We show that key elements of $H$ needed to construct such an isomorphism $\\varphi$, such as those whose image under $\\varphi$ is an $n$-cycle or $(n-1)$-cycle, can be recognised with high probability by the lengths of just four of their cycles in $\\Lambda$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6586","kind":"arxiv","version":3},"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"}