{"paper":{"title":"Invariable generation with elements of coprime prime-power order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrea Lucchini, Eloisa Detomi","submitted_at":"2014-09-03T08:58:51Z","abstract_excerpt":"A finite group $G$ is coprimely-invariably generated if there exists a set of generators $\\{g_1, \\ldots, g_d\\}$ of $G$ with the property that the orders $|g_1|, \\ldots, |g_d|$ are pairwise coprime and that for all $x_1, \\ldots, x_d \\in G$ the set $\\{g_1^{x_1}, \\ldots, g_d^{x_d}\\}$ generates $G$. In the particular case when $|g_1|, \\ldots, |g_d|$ can be chosen to be prime-powers we say that $G$ is prime-power coprimely-invariably generated. We will discuss these properties, proving also that the second one is stronger than the first, but that in the particular case of finite soluble groups they"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0997","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"}