{"paper":{"title":"On one generalization of finite nilpotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander N. Skiba, Zhang Chi","submitted_at":"2018-01-28T14:15:03Z","abstract_excerpt":"Let $\\sigma =\\{\\sigma_{i} | i\\in I\\}$ be a partition of the set $\\Bbb{P}$ of all primes and $G$ a finite group. A chief factor $H/K$ of $G$ is said to be $\\sigma$-central if the semidirect product $(H/K)\\rtimes (G/C_{G}(H/K))$ is a $\\sigma_{i}$-group for some $i=i(H/K)$. $G$ is called $\\sigma$-nilpotent if every chief factor of $G$ is $\\sigma$-central. We say that $G$ is semi-${\\sigma}$-nilpotent (respectively weakly semi-${\\sigma}$-nilpotent) if the normalizer $N_{G}(A)$ of every non-normal (respectively every non-subnormal)   $\\sigma$-nilpotent subgroup $A$ of $G$ is $\\sigma$-nilpotent. In t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09235","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"}