{"paper":{"title":"On the lattice of subracks of the rack of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.QA"],"primary_cat":"math.CO","authors_text":"Istvan Heckenberger, John Shareshian, Volkmar Welker","submitted_at":"2015-12-04T15:47:05Z","abstract_excerpt":"In this paper we initiate the study of racks from the combined perspective of combinatorics and finite group theory. A rack R is a set with a self-distributive binary operation. We study the combinatorics of the partially ordered set {\\cal R}(R) of all subracks of R with inclusion as the order relation. Groups G with the conjugation operation provide an important class of racks. For the case R = G we show that\n  -> the order complex of {\\cal R}(R) has the homotopy type of a sphere,\n  -> the isomorphism type of {\\cal R}(R) determines if G is abelian, nilpotent, supersolvable, solvable or simple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01459","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"}