{"paper":{"title":"Groups whose non-normal subgroups are either nilpotent or minimal non-nilpotent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Hamid Mousavi, Nasrin Dastborhan","submitted_at":"2023-11-01T07:58:45Z","abstract_excerpt":"Let $\\mathfrak{Nil}$ be the class of nilpotent groups and $G$ be a group. We call $G$ a meta-$\\mathfrak{Nil}$-Hamiltonian group if any of its non-$\\mathfrak{Nil}$ subgroups is normal. Also, we call $G$ a para-$\\mathfrak{Nil}$-Hamiltonian group if $G$ is a non-$\\mathfrak{Nil}$ group and every non-normal subgroup of $G$ is either a $\\mathfrak{Nil}$-group or a minimal non-$\\mathfrak{Nil}$ group. In this paper we investigate the class of finitely generated meta-$\\mathfrak{Nil}$-Hamiltonian and para-$\\mathfrak{Nil}$-Hamiltonian groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.00352","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.00352/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}