On a class of non-solvable groups

JOURNAL OF ALGEBRA

卷:496

Article

Miao, Long¹  Zhang, Jia^1,2 

[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China

[2] China West Normal Univ, Sch Math & Informat, Nanchong 637009, Peoples R China

关键词: M-supplemented subgroups;    Chief factor;    Composition factor;    Simple groups;   

DOI  :  10.1016/j.jalgebra.2017.10.016

来源: Elsevier

【 摘 要 】

In this paper, we use the properties of subgroups with given order to study the structure of finite groups. The main result is as follows: Let G be a group and P be a Sylow p-subgroup of G. Suppose that 1 < d <= vertical bar P vertical bar If every subgroup H of P with vertical bar H vertical bar = d is M-supplemented in G, then every non-abelian pd-G-chief factor A/B satisfies one of the following conditions: (1) A/B congruent to PSL(2, 7) and p = 7; A/B congruent to PSL(2, 11) and p = 11; (2) A/B congruent to PSL(2, 2(i)) and p = 2(t) + 1 > 3 is a Fermat prime; (3) A/B congruent to PSL(n, q), n >= 3 is a prime, (n, q - 1) = 1 and p = q(n) -1/q-1; (4) A/B congruent to M-11 and p = 11; A/B congruent to M-23 and p = 23; (5) A/B congruent to A(p) and p >= 5. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free