| 极小子群的超中心性与幂零群 |
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| 引用本文： | 刘玉凤.极小子群的超中心性与幂零群[J].高师理科学刊,2008,28(6). |
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| 作者姓名： | 刘玉凤 |
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| 作者单位： | 山东工商学院,数学与信息科学学院,山东,烟台,264005 |
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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： | 利用完全c-可换子群的概念,得到了幂零群的2个充分条件:(1)如果群G的4阶循环子群在G中完全c-可换且G的任意极小子群含于Z∞(G)中,那么G是幂零群;(2)设N■G且G/N是幂零群.如果N的任意4阶循环子群在G中完全c-可换且N的任意极小子群包含在Z∞(G)中,那么G是幂零群.
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| 关 键 词： | 有限群 完全c-可换子群 极小子群 幂零群 |
Hypercenter of minimal subgroups and nilpotent group |
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| LIU Yu-feng.Hypercenter of minimal subgroups and nilpotent group[J].Journal of Science of Teachers＇College and University,2008,28(6). |
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| Authors: | LIU Yu-feng |
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| Abstract: | Using the concept,completely c-permutable subgroup of finite groups,two sufficient conditions of nilpotent groups was obtained:(1)If any cyclic subgroup ofG of order 4 is completely c-permutable inG and any minimal subgroup ofG is contained in the hypercenter ofG,thenG is a nilpotent group.(2)Let N be a normal subgroup ofG and G Nbe a nilpotent group.If any cyclic subgroup of N of order 4 is completely c-permutable inG and any minimal subgroup of N is contained in hypercenter ofG,thenG is a nilpotent group. |
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| Keywords: | finite group c-permutable subgroup minimal subgroup nilpotent group |
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