| c-幂零群与幂零群 |
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| 引用本文： | 冯海辉.c-幂零群与幂零群[J].上海海事大学学报,2012,33(2):100-102. |
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| 作者姓名： | 冯海辉 |
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| 作者单位： | 上海海事大学文理学院,上海,201306 |
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| 基金项目： | 国家自然科学基金 (11101268) |
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| 摘 要： | 为研究有限群的幂零性,利用群的不可约特征标,定义一类新群——c-幂零群.给出一个群G为c-幂零群的充分必要条件:对G的每个不可约特征标χ∈Irr(G),只要Kerχ∈Δ,就有G/Kerχ为c-幂零群.讨论c-幂零群与幂零群之间的关系.
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| 关 键 词： | c-幂零群 幂零群 不可约特征标 |
| 收稿时间： | 9/21/2011 8:33:45 AM |
| 修稿时间： | 2/6/2012 4:44:24 PM |
c-nilpotent group and nilpotent group |
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| Feng Haihui.c-nilpotent group and nilpotent group[J].Journal of Shanghai Maritime University,2012,33(2):100-102. |
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| Authors: | Feng Haihui |
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| Institution: | Department of Mathematics, Shanghai Maritime University |
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| Abstract: | To study the nilpotency of a finite group,a new class of finite group called c-nilpotent group is defined by using the irreducible characters of finite groups.A sufficient and necessary condition for a group G to be a c-nilpotent group is given: for any irreducible character χ∈Irr(G),G/Kerχ is a c-nilpotent group so long as Kerχ∈Δ.The relationship between the c-nilpotent group and the nilpotent group is explored. |
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| Keywords: | c-nilpotent group nilpotent group irreducible character |
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