On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups

Сибирский математический журнал

D. O. Revin¹  W. Guo²  N. V. Maslova³ 

[1] Novosibirsk State University;University of Science and Technology of China;Ural Federal University

关键词: finite group;    pronormal subgroup;    Sylow 2-subgroup;    subgroup of odd index;    wreath product;    direct product;    self-normalizing subgroup;    simple group;    symplectic group;   

DOI  :  10.1134/S0037446618040043

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We study finite groups with the following property (*): All subgroups of odd index are pronormal. Suppose that G has a normal subgroup A with property (*), and the Sylow 2-subgroups of G/A are self-normalizing. We prove that G has property (*) if and only if so does NG(T)/T, where T is a Sylow 2-subgroup of A. This leads to a few results that can be used for the classification of finite simple groups with property (*).

【 授权许可】

CC BY