{"paper":{"title":"On two questions from the Kourovka Notebook concerning maximal subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Antonio Beltr\\'an, Fernando Viudez","submitted_at":"2026-07-07T16:02:31Z","abstract_excerpt":"Let \\(p\\) be a prime number. When \\(p\\) is odd, we study finite groups in which every maximal subgroup is either non-abelian simple or \\(p\\)-nilpotent, as well as those in which every maximal subgroup is either non-abelian simple or \\(p\\)-decomposable. We prove that every non-simple, non-solvable group satisfying these criteria is \\(p\\)-nilpotent, and \\(p\\)-decomposable, respectively. This answers two open questions posed by V.S. Monakhov and I.N. Tyutyanov in the Kourovka Notebook. Additionally, if \\(p=2\\), we improve the main result of Monakhov and Tyutyanov by providing a complete classific"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06434","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06434/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"}