Abstract
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.
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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
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Shi, J.T., Zhang, C. Some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable. Acta. Math. Sin.-English Ser. 27, 891–896 (2011). https://doi.org/10.1007/s10114-011-9476-1
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DOI: https://doi.org/10.1007/s10114-011-9476-1