{"paper":{"title":"The second maximal groups with respect to the sum of element orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Marcel Herzog, Mercede Maj, Patrizia Longobardi","submitted_at":"2019-01-28T14:13:53Z","abstract_excerpt":"Denote by $G$ a finite group and let $\\psi(G)$ denote the sum of element orders in $G$. In 2009, H.Amiri, S.M.Jafarian Amiri and I.M.Isaacs proved that if $|G|=n$ and $G$ is non-cyclic, then $\\psi(G)<\\psi(C_n)$, where $C_n$ denotes the cyclic group of order $n$. In 2018 we proved that if $G$ is non-cyclic group of order $n$, then $\\psi(G)\\leq \\frac 7{11}\\psi(C_n)$ and equality holds if $n=4k$ with $(k,2)=1$ and $G=(C_2\\times C_2)\\times C_k$. In this paper we proved that equality holds if and only if $n$ and $G$ are as indicated above. Moreover we proved the following generalization of this res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09662","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"}