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《Journal of Guangxi Normal University(Natural Science Edition)》 2017-01
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Influence of the Number of Conjugacy Classes of Nonsubnormal Subgroups on the Structure of Finite Groups

ZHONG Xianggui;DING Ruifang;LING Simin;College of Mathematics and Statistics,Guangxi Normal University;  
Let G be a finite group,π(G)be the set of prime factors dividing|G|andμ(G)denote the number of conjugacy classes of all non-subnormal subgroups of G.In this paper,it is shown that all finite groups G withμ(G)≤2|π(G)|are solvable and that the structure of finite groups having at most|π(G)|conjugacy classes of non-subnormal subgroups are completely characterized.
【Fund】: 国家自然科学基金(11261007 11461007);; 广西自然科学基金(2014GXNSFAA118009);; 广西教育厅科研项目(ZD2014016 KY2015YB504)
【CateGory Index】: O152.1
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【References】
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1 LU Jiakuan;LIU Xuexia;QIN Xueqing;College of Mathematics and Statistics,Guangxi Normal University;;Notes on Frobenius Groups[J];广西师范大学学报(自然科学版);2018-01
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【Co-citations】
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1 ZHONG Xianggui;DING Ruifang;LING Simin;College of Mathematics and Statistics,Guangxi Normal University;;Influence of the Number of Conjugacy Classes of Nonsubnormal Subgroups on the Structure of Finite Groups[J];广西师范大学学报(自然科学版);2017-01
2 ZUO Lin;GUO Pengfei;Dept of Math,Lianyungang Coll of Jiangsu Norm Univ;;Some results on subnormal subgroups of finite groups[J];扬州大学学报(自然科学版);2014-01
3 FENG Ai-fang, LIU Zu-hua Department of Mathematics, Kunming University, Kunming 650214, China;Finite Groups Havingat Most Eight Non-subnormal Subgroups[J];西南师范大学学报(自然科学版);2012-02
4 LIU Hui-feng1,YANG Dong-hui2(1.School of Mathematics,Xinzhou Teacher's University,Xinzhou 034000,P.R.C.;2.School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,P.R.C.);On the subgroups of A_5[J];西南民族大学学报(自然科学版);2012-01
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【Co-references】
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1 ZHONG Xianggui;DING Ruifang;LING Simin;College of Mathematics and Statistics,Guangxi Normal University;;Influence of the Number of Conjugacy Classes of Nonsubnormal Subgroups on the Structure of Finite Groups[J];广西师范大学学报(自然科学版);2017-01
2 LU Jiakuan;QIU Yanyan;College of Mathematics and Statistics,Guangxi Normal University;;The Influence of Weakly s-supplemented Subgroups on Solvability of Finite Groups[J];广西师范大学学报(自然科学版);2017-01
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