{"paper":{"title":"Monochromatic generating sets in groups and other algebraic structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Boaz Tsaban, Itay Ravia, Noam Lifshitz","submitted_at":"2012-11-26T16:43:28Z","abstract_excerpt":"The \\emph{generating chromatic number} of a group $G$, $\\chigen(G)$, is the maximum number of colors $k$ such that there is a monochromatic generating set for each coloring of the elements of $G$ in $k$ colors. If no such maximal $k$ exists, we set $\\chigen(G)=\\infty$. Equivalently, $\\chigen(G)$ is the maximal number $k$ such that there is no cover of $G$ by proper subgroups ($\\infty$ if there is no such maximal $k$).\n  We provide characterizations, for arbitrary gruops, in the cases $\\chigen(G)=\\infty$ and $\\chigen(G)=2$. For nilpotent groups (in particular, for abelian ones), all possible ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6016","kind":"arxiv","version":3},"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"}