关于p-可解群的二极大子群  

On second maximal subgroups of p -solvable groups

作　　者：缪龙[1] 陈龙 赵瑜 鲍宏伟[3] MIAO Long;CHEN Long;ZHAO Yu;BAO Hongwei(School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,China;Basic Course Department,Jiangsu Vocational College of Information Technology,Wuxi 214153,China;Faculty of Science,Bengbu University,Bengbu 233030,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002 [2]江苏信息职业技术学院基础课部,江苏无锡214153 [3]蚌埠学院理学院,安徽蚌埠233030

出　　处：《西北大学学报（自然科学版）》2020年第2期261-264,共4页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11871062);江苏省自然科学基金资助项目(BK20181451)。

摘　　要：文中研究了有限p-可解群中二极大子群的相关性质。采用极小阶反例的方法,并结合极大子群的指数,得出p-可解群中强二极大子群的判别条件,同时还探讨了弱二极大子群本身的性质。从而揭示了二极大子群对p-可解群结构的重要影响。In this paper,the properties of second maximal subgroups in finite p-solvable groups have been studied.By using the method of counterexample of minimal order and combining with the indices of maximal subgroups,the criterion of strong second maximal subgroups in p-solvable groups has been obtained and further the properties of weak second maximal subgroups have been discussed.Hence the influences of second maximal subgroups on the structure of p-solvable groups have been revealed.

关 键 词：P-可解群 极大子群 二极大子群 CAP-子群 

分 类 号：O152.1[理学—数学]