{"paper":{"title":"Relative n-isoclinism classes and relative n-th nilpotency degree of finite groups","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ahmad Erfanian (Ferdowsi University of Mashhad, Francesco G. Russo (Universita' degli Studi di Palermo, Iran), Italy), Malayer, Mashhad, Palermo, Rashid Rezaei (University of Malayer","submitted_at":"2010-03-11T11:16:02Z","abstract_excerpt":"The purpose of the present paper is to consider the notion of isoclinism between two finite groups and its generalization to n-isoclinism, introduced by J. C. Bioch in 1976. A weaker form of n-isoclinism, called relative n-isoclinism, will be discussed. This will allow us to improve some classical results in literature. We will point out the connections between a relative n-isoclinism and the notions of commutativity degree, n-th nilpotency degree and relative n-th nilpotency degree, which arouse interest in the classification of groups of prime power order in the last years."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2306","kind":"arxiv","version":3},"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"}