| 非幂零极大子群共轭类类数给定的有限群 |
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| 引用本文： | 史江涛,张翠,申振才. 非幂零极大子群共轭类类数给定的有限群[J]. 数学的实践与认识, 2013, 43(7) |
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| 作者姓名： | 史江涛 张翠 申振才 |
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| 作者单位： | 1. 烟台大学数学与信息科学学院,山东烟台,264005
2. 北京大学数学科学学院,北京,100871 |
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| 基金项目： | 国家自然科学基金，中国博士后科学基金 |
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| 摘 要： | 证明了非幂零极大子群共轭类类数等于2的有限群必可解,并给出了非幂零极大子群同阶类类数等于2的非可解群的等价刻画.
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| 关 键 词： | 有限群 幂零极大子群 可解群 |
Finite Groups with a Given Number of Conjugacy Classes of Non-nilpotent Maximal Subgroups |
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| SHI Jiang-tao , ZHANG Cui , SHEN Zhen-cai. Finite Groups with a Given Number of Conjugacy Classes of Non-nilpotent Maximal Subgroups[J]. Mathematics in Practice and Theory, 2013, 43(7) |
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| Authors: | SHI Jiang-tao ZHANG Cui SHEN Zhen-cai |
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| Abstract: | In this paper,we prove that a finite group with exactly two conjugacy classes of non-nilpotent maximal subgroups is solvable.Furthermore,we give an equivalent characterization of a finite non-solvable group with exactly two classes of non-nilpotent maximal subgroups of the same order. |
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| Keywords: | finite group nilpotent maximal subgroup solvable group |
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