{"paper":{"title":"On the Davenport constant and group algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Daniel Smertnig","submitted_at":"2009-07-28T13:27:17Z","abstract_excerpt":"For a finite abelian group $G$ and a splitting field $K$ of $G$, let $d(G, K)$ denote the largest integer $l \\in \\N$ for which there is a sequence $S = g_1 \\cdot ... \\cdot g_l$ over $G$ such that $(X^{g_1} - a_1) \\cdot ... \\cdot (X^{g_l} - a_l) \\ne 0 \\in K[G]$ for all $a_1, ..., a_l \\in K^{\\times}$. If $D(G)$ denotes the Davenport constant of $G$, then there is the straightforward inequality $D(G)-1 \\le d (G, K)$. Equality holds for a variety of groups, and a standing conjecture of W. Gao et.al. states that equality holds for all groups. We offer further groups for which equality holds, but we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4913","kind":"arxiv","version":2},"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"}