Some Sufficient Conditions on the Number of Non-abelian Subgroups of a Finite Group to be Solvable  

作　　者：Jiang Tao SHI Cui ZHANG 

机构地区：[1]LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China [2]University of Primorska, FAMNIT, Glagoljaska 8, 6000 Koper, Slovenia [3]University of Primorska, PINT, Muzejski trg 2, 6000 Koper, Slovenia

出　　处：《Acta Mathematica Sinica,English Series》2011年第5期891-896,共6页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant No. 10871032）, China Postdoctoral Science Foundation （Grant No. 20100470136）; the second author is supported in part by ＂Agencija za raziskovalno dejavnost Republike Slovenije＂, proj. mladi raziskovalci, ＂Agencija za raziskovalno dejavnost Republike Slovenije＂, Research Program P1-0285

摘　　要：Thompson＇s theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important application of Thompson＇s theorem, a finite group is solvable if it has an abelian maximal subgroup. In this paper, we give some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable.Thompson＇s theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important application of Thompson＇s theorem, a finite group is solvable if it has an abelian maximal subgroup. In this paper, we give some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable.

关 键 词：Finite group abelian subgroup solvable group 

分 类 号：O186.1[理学—数学] O152.1[理学—基础数学]