{"paper":{"title":"On the algebraic and arithmetic structure of the monoid of product-one sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Jun Seok Oh","submitted_at":"2018-02-03T15:31:38Z","abstract_excerpt":"Let $G$ be a finite group. A finite unordered sequence $S = g_1 \\boldsymbol{\\cdot} \\ldots \\boldsymbol{\\cdot} g_{\\ell}$ of terms from $G$, where repetition is allowed, is a product-one sequence if its terms can be ordered such that their product equals $1_G$, the identity element of the group. As usual, we consider sequences as elements of the free abelian monoid $\\mathcal F (G)$ with basis $G$, and we study the submonoid $\\mathcal B (G) \\subset \\mathcal F (G)$ of all product-one sequences. This is a finitely generated C-monoid, which is a Krull monoid if and only if $G$ is abelian. In case of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00991","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"}