{"paper":{"title":"Partitions of groups into large subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Igor Protasov, Sergii Slobodianiuk","submitted_at":"2014-08-24T13:45:31Z","abstract_excerpt":"Let G be a group and let k be a cardinal. A subset A of G is called left (right) k-large if there exists a subset F of G such that |F| < { and G = FA (G = AF). We say that A is k-large if A is left and right k-large. It is known that every infinite group G can be partitioned into countably many \\aleph_0-large subsets. On the other hand, every amenable (in particular Abelian) group G cannot be partitioned into > \\aleph_0 \\aleph_0-large subsets. We prove that every infinite group G of cardinality k can be partitioned into k left- \\aleph_1-large subsets and every free group F_k in the infinite al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5606","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"}