{"paper":{"title":"On a conjecture of Street and Whitehead on locally maximal product-free sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Chimere S. Anabanti, Sarah B. Hart","submitted_at":"2015-06-08T10:27:47Z","abstract_excerpt":"Let $S$ be a non-empty subset of a group $G$. We say $S$ is product-free if $S\\cap SS=\\varnothing$, and $S$ is locally maximal if whenever $T$ is product-free and $S\\subseteq T$, then $S=T$. Finally $S$ fills $G$ if $G^*\\subseteq S \\sqcup SS$ (where $G^*$ is the set of all non-identity elements of $G$), and $G$ is a filled group if every locally maximal product-free set in $G$ fills $G$. Street and Whitehead (in `Group Ramsey Theory', J. Comb. Theory Series A, 17 (1974) 219-226) investigated filled groups and gave a classification of filled abelian groups. In this paper, we obtain some results"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02430","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"}