| 完全条件置换子群对有限群结构的影响 |
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| 引用本文： | 陶司兴,薛瑞雪,郭秀云. 完全条件置换子群对有限群结构的影响[J]. 苏州大学学报(医学版), 2009, 25(3): 5-8 |
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| 作者姓名： | 陶司兴 薛瑞雪 郭秀云 |
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| 作者单位： | 陶司兴(商丘师范学院,数学系,河南,商丘,476000;上海大学,理学院,上海,200444);薛瑞雪,郭秀云(信阳师范学院,计算机与信息技术学院,河南,信阳,464000) |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 有限群G的子群H称为G的完全条件置换子群，如果对于G的任一子群K，存在x∈（H，K），使得HK^z=K^zH文中利用完全条件置换子群对有限群结构的影响，给出了超可解群的若干充分条件，并将一些结果进行了推广．
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| 关 键 词： | 完全条件置换子群 群系 超可解群 |
Influence of completely conditionally permutable subgroups on the structure of finite groups |
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| Tao Sixing,,Xue Ruixue,Guo Xiuyun. Influence of completely conditionally permutable subgroups on the structure of finite groups[J]. Journal of Suzhou University(Natural Science), 2009, 25(3): 5-8 |
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| Authors: | Tao Sixing Xue Ruixue Guo Xiuyun |
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| Affiliation: | 1.Dept.of Mathematics;Shangqiu Normal Univ.;Shangqiu 476000;China;2.School of Computer and Information Technology;Xingyang Normal Univ.;Xinyang 464000;3.School of Sciences;Shanghai Univ.;Shanghai 200444;China |
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| Abstract: | A subgroup H of a finite group G is said to be completely conditionally permutable in G if for every subgroup K of G,there exists an element x ∈ 〈H,K〉 such that HK^z=K^zH. Some sufficient conditions for a group to be supersoluble are obtained by using the influence of completely conditionally permutable subgroups on the structure of finite groups, and some results are generalized. |
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| Keywords: | completely conditionally permutable subgroups formation supersoluble groups |
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