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.
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
