Normal sections, class sizes and solvability of finite groups

JOURNAL OF ALGEBRA

卷:399

Article

Akhlaghi, Zeinab¹  Beltran, Antonio²  Jose Felipe, Maria³ 

[1] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, ZA-3209 Pietermaritzburg, South Africa

[2] Univ Jaume 1, Dept Matemat, Castellon de La Plana 12071, Spain

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

关键词: Finite groups;    Conjugacy class sizes;    Normal sections;    Solvability;   

DOI  :  10.1016/j.jalgebra.2013.09.033

来源: Elsevier

【 摘 要 】

If G is a finite group, we show that any normal subgroup of G which has exactly three G-conjugacy class sizes is solvable. Thus, we give an extension for normal subgroups of the classical N. Ito's theorem which asserts that those finite groups having three class sizes are solvable, and particularly, a new proof of it is provided. In order to do this, we investigate the structure of a normal section N/K of G such that every element in N lying outside of K has the same G-class size. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free