On SS-quasinormal subgroups and the structure of finite groups

作     者：WEI XianBiao1,2 & GUO XiuYun2, 1Department of Mathematics and Physics, Anhui Institute of Architecture and Industry, Hefei 230022, China 2Department of Mathematics, Shanghai University, Shanghai 200444, China 

作者机构：Department of Mathematics and Physics Anhui Institute of Architecture and Industry Hefei China Department of Mathematics Shanghai University Shanghai China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2011年第54卷第3期

页      面：449-456页

核心收录：

学科分类：083002[工学-环境工程] 0830[工学-环境科学与工程（可授工学、理学、农学学位）] 07[理学] 08[工学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No. 10771132) the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200802800011) the Research Grant of Shanghai University, Shanghai Leading Academic Discipline Project (Grant No. J50101) Natural Science Foundation of Anhui Province (Grant No.KJ2008A030) 

主　　题：S-quasinormal subgroups SS-quasinormal subgroups p-nilpotent groups supersolvable groups 

摘      要：A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpotent if there is a subgroup D of P with 1 |D| |P| such that every subgroup of P with order |D| or 2|D| whenever p = 2 and |D| = 2 is SS-quasinormal in G, where p is the smallest prime dividing the order of G and P is a Sylow p-subgroup of G.