On the Frattini subgroup of a finite group

JOURNAL OF ALGEBRA

卷:470

Article

Aivazidis, Stefanos¹  Ballester-Bolinches, Adolfo¹ 

[1] Univ Valencia, Dept Algebra, C Dr Moliner 50, E-46100 Valencia, Spain

关键词: Frattini subgroup;    Formations of groups;   

DOI  :  10.1016/j.jalgebra.2016.09.010

来源: Elsevier

【 摘 要 】

We study the class of finite groups G satisfying Phi(G/N) = Phi(G)N/N for all normal subgroups N of G. As a consequence of our main results we extend and amplify a theorem of Doerk concerning this class from the soluble universe to all finite groups and answer in the affirmative a long-standing question of Christensen whether the class of finite groups which possess complements for each of their normal subgroups is subnormally closed. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free