{"paper":{"title":"Zero-separating invariants for finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jonathan Elmer, Martin Kohls","submitted_at":"2013-08-05T14:29:22Z","abstract_excerpt":"We fix a field $\\kk$ of characteristic $p$. For a finite group $G$ denote by $\\delta(G)$ and $\\sigma(G)$ respectively the minimal number $d$, such that for any finite dimensional representation $V$ of $G$ over $\\kk$ and any $v\\in V^{G}\\setminus\\{0\\}$ or $v\\in V\\setminus\\{0\\}$ respectively, there exists a homogeneous invariant $f\\in\\kk[V]^{G}$ of positive degree at most $d$ such that $f(v)\\ne 0$. Let $P$ be a Sylow-$p$-subgroup of $G$ (which we take to be trivial if the group order is not divisble by $p$). We show that $\\delta(G)=|P|$. If $N_{G}(P)/P$ is cyclic, we show $\\sigma(G)\\ge|N_{G}(P)|$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0991","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"}