The Influence of s-Conditional Permutability of Subgroups on the Structure of Finite Groups  

作　　者：Wen Juan NIU Wen Bin GUO Yu Feng LIU 

机构地区：[1]Department of Mathematics, Xuzhou Normal University, Jiangsu 221116, P. R. China [2]Department of Mathematics, University of Science and Technology of China, Anhui 230026, P. R. China [3]School of Mathematical and Informational Science, Shandong Institute of Business and Technology, Shandong 264005, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第1期173-179,共7页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.11071229);the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No.10KJD110004);the Postgraduate Innovation Grant of Xuzhou Normal University

摘　　要：Let G be a finite group. Fix a prime divisor p of IGI and a Sylow p-subgroup P of G, let d be the smallest generator number of P and Ma（P） denote a family of maximal subgroups P1, P2 , Pd of P satisfying ∩^di=1 Pi = Ф（P）, the Frattini subgroup of P. In this paper, we shall investigate the influence of s-conditional permutability of the members of some fixed .Md（P） on the structure of finite groups. Some new results are obtained and some known results are generalized.Let G be a finite group. Fix a prime divisor p of IGI and a Sylow p-subgroup P of G, let d be the smallest generator number of P and Ma（P） denote a family of maximal subgroups P1, P2 , Pd of P satisfying ∩^di=1 Pi = Ф（P）, the Frattini subgroup of P. In this paper, we shall investigate the influence of s-conditional permutability of the members of some fixed .Md（P） on the structure of finite groups. Some new results are obtained and some known results are generalized.

关 键 词：finite groups s-conditionally permutable groups saturated formations supersoluble groups nilpotent groups. 

分 类 号：O151.2[理学—数学]