A class of generalised finite T-groups

JOURNAL OF ALGEBRA

卷:333

Article

Ballester-Bolinches, A.¹  Feldman, A. D.²  Pedraza-Aguilera, M. C.³  Ragland, M. F.⁴ 

[1] Univ Valencia, Dept Algebra, E-46100 Valencia, Spain

[2] Franklin & Marshall Coll, Dept Math, Lancaster, PA 17604 USA

[3] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain

[4] Auburn Univ, Dept Math, Montgomery, AL 36124 USA

关键词: T-group;    Formation;    F-subnormal subgroup;    Subnormal subgroup;    Pronormal subgroup;   

DOI  :  10.1016/j.jalgebra.2011.02.018

来源: Elsevier

【 摘 要 】

Let F be a formation (of finite groups) containing all nilpotent groups such that any normal subgroup of any T-group in F and any subgroup of any soluble T-group in F belongs to F. A subgroup M of a finite group G is said to be a-normal in G if G/Core(G)(M) belongs to F. Named after Kegel, a subgroup U of a finite group G is called a K-F-subnormal subgroup of G if either U = G or U = U(0) <= U(1) <= ... <= U(n) = G such that U(i-1) is either normal in U(i) or U(i-1) is F-normal in U(i), for i = 1, 2, ... ,n. We call a finite group G a T(F)-group if every K-F-subnormal subgroup of G is normal in G. When a is the class of all finite nilpotent groups, the T(F)-groups are precisely the T-groups. The aim of this paper is to analyse the structure of the T(F)-groups and show that in many cases T(F) is much more restrictive than T. (c) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free