弱次正规子群和有限群的可解性 |
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引用本文: | 李士恒,梁登峰.弱次正规子群和有限群的可解性[J].数学的实践与认识,2014(16). |
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作者姓名: | 李士恒 梁登峰 |
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作者单位: | 郑州航空工业管理学院数理系;北京工商大学理学院; |
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基金项目: | 国家自然科学基金(11171364);北京工商大学青年教师科研启动基金(QNJJ2011-50) |
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摘 要: | 如果群G有次正规子群K使HK⊿⊿G且H∩K⊿⊿G,那么子群H被称做群G的弱次正规子群.利用极大子群Sylow子群或Sylow子群正规化子的子群的弱次正规性得到了一些关于有限群的可解性结论.
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关 键 词: | 有限群 弱次正规 几乎正规 弱c-正规 极大子群 |
Weakly Subnormal Subgroups and The Sovability of Finite Groups |
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Abstract: | H is called a weakly subnormal subgroup of G,if there exists a subnormal subgroup K of G such that H∩K⊿⊿G and HK⊿⊿G.We get some results on the solvability of finite groups with weakly subnormal subgroups of maximal subgroup,Sylow subgroup or normalizer of sylow subgroup. |
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Keywords: | finite group weakly subnormal subgroups weakly c-normal maximal subgroups |
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