Π-Quasinormally embedded subgroups and p-nilpotency of finite groups. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Xu, Yong; Chen, Guiyun
• Is Part Of: Communications in algebra. Volume 49:Issue 1(2021)
• Page Start: 421
• Page End: 426
• Publication Date: 2021-01-02
• Subjects: Finite group -- p-nilpotency -- π-quasinormally embedded subgroup; 20D10 -- 20D15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1800721
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let P be a nontrivial p -group. A chain of subgroups 1 = P 0 ≨ P 1 ≨ ⋯ ≨ P n = P is called a maximal chain of P provided that | P i : P i − 1 | = p, i = 1, 2, …, n . In this article, we determine the structure of finite groups having π -quasinormally embedded subgroups of a maximal chain of Sylow subgroups. We obtain new characterizations of finite p -nilpotent and supersolvable groups.