Supersolubility of a Finite Group with Normally Embedded Maximal Subgroups in Sylow Subgroups

Сибирский математический журнал

V. S. Monakhov¹  A. A. Trofimuk² 

[1] Francisk Skorina Gomel State University;Pushkin Brest State University

关键词: p-supersoluble group;    normally embedded subgroup;    maximal subgroup;    Sylow subgroup;   

DOI  :  10.1134/S0037446618050166

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

Let P be a subgroup of a Sylow subgroup of a finite group G. If P is a Sylow subgroup of some normal subgroup of G then P is called normally embedded in G. We establish tests for a finite group G to be p-supersoluble provided that every maximal subgroup of a Sylow p-subgroup of X is normally embedded in G. We study the cases when X is a normal subgroup of G, X = Op',p(H), and X = F*(H) where H is a normal subgroup of G.

【 授权许可】

CC BY