{"paper":{"title":"On the Erdos-Ko-Rado property for finite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Keivan Mallahi-Karai, Mohammad Bardestani","submitted_at":"2013-10-06T22:56:18Z","abstract_excerpt":"Let a finite group $G$ act transitively on a finite set $X$. A subset $S\\subseteq G$ is said to be {\\it intersecting} if for any $s_1,s_2\\in S$, the element $s_1^{-1}s_2$ has a fixed point. The action is said to have the {\\it weak Erd\\H{o}s-Ko-Rado} property, if the cardinality of any intersecting set is at most $|G|/|X|$. If, moreover, any maximal intersecting set is a coset of a point stabilizer, the action is said to have the {\\it strong Erd\\H{o}s-Ko-Rado} property. In this paper we will investigate the weak and strong Erd\\H{o}s-Ko-Rado property and attempt to classify the groups whose all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1643","kind":"arxiv","version":5},"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"}