{"paper":{"title":"A result on the sum of element orders of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Afsaneh Bahri, Behrooz Khosravi, Zeinab Akhlaghi","submitted_at":"2019-03-31T14:44:06Z","abstract_excerpt":"Let $G$ be a finite group and $\\psi(G)=\\sum_{g\\in{G}}{o(g)}$. There are some results about the relation between $\\psi(G)$ and the structure of $G$. For instance, it is proved that if $G$ is a group of order $n$ and $\\psi(G)>\\dfrac{211}{1617}\\psi(C_n)$, then $G$ is solvable. Herzog {\\it{et al.}} in [Herzog {\\it{et al.}}, Two new criteria for solvability of finite groups, J. Algebra, 2018] put forward the following conjecture:\n  \\noindent{\\bf Conjecture.} {\\it {If $G$ is a non-solvable group of order $n$, then $${\\psi(G)}\\,{\\leq}\\,{{\\dfrac{211}{1617}}{\\psi(C_n)}}$$ with equality if and only if $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00425","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"}