{"paper":{"title":"Restricted Sumsets in Finite Nilpotent Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.CO","authors_text":"Hao Pan, Shanshan Du","submitted_at":"2012-06-27T02:57:32Z","abstract_excerpt":"Suppose that $A,B$ are two non-empty subsets of the finite nilpotent group $G$. If $A\\not=B$, then the cardinality of the restricted sumset $$A\\dotplus B={a+b: a\\in A, b\\in B, a\\neq b} $$ is at least $$\\min{p(G),|A|+|B|-2},$$ where $p(G)$ denotes the least prime factor of $|G|$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6160","kind":"arxiv","version":6},"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"}