Permutability of injectors with a central socle in a finite solvable group

JOURNAL OF ALGEBRA

卷:476

Article

Dark, Rex¹  Feldman, Arnold D.²  Dolores Perez-Ramos, Maria³ 

[1] Natl Univ Ireland, Sch Math Stat & Appl Math, Univ Rd, Galway, Ireland

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

[3] Univ Valencia, Dept Matemat, C-Doctor Moliner 50, Burjassot 46100, Spain

关键词: Finite solvable group theory;    Fitting class;    Injector;    Central socle;   

DOI  :  10.1016/j.jalgebra.2016.11.041

来源: Elsevier

【 摘 要 】

In response to an Open Question of Doerk and Hawkes [5, IX Section 3, page 615], we shall show that if Z(pi) is the Fitting class formed by the finite solvable groups whose 7r-socle is central (where pi is a set of prime numbers), then the Zff-injectors of a finite solvable group G permute with the members of a Sylow basis in G. The proof depends on the properties of certain extraspecial groups [4]. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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