Some new characterizations of PST-groups

JOURNAL OF ALGEBRA

卷:399

Article

Yi, Xiaolan¹  Skiba, Alexander N.² 

[1] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

[2] Francisk Skorina Gomel State Univ, Dept Math, Gomel 246019, BELARUS

关键词: Finite group;    Quasipermutable subgroup;    PST-group;    Hall subgroup;    Supersoluble group;    Gaschutz subgroup;    Carter subgroup;    Saturated formation;   

DOI  :  10.1016/j.jalgebra.2013.10.001

来源: Elsevier

【 摘 要 】

Let H and B be subgroups of a finite group G such that G = N-G(H)B. Then we say that H is quasipermutable (respectively, S-quasipermutable) in G provided H permutes with B and with every subgroup (respectively, with every Sylow subgroup) A of B such that (vertical bar H vertical bar, vertical bar A vertical bar) = 1. In this paper we analyze the influence of S-quasipermutable and quasipermutable subgroups on the structure of G. As an application, we give new characterizations of soluble PST-groups. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free