有限n-正规化子群 |
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作者单位: | 北京大学数学科学学院,首都师范大学数学科学学院 |
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摘 要: | 基于Ashrafi的想法,定义了n-正规化子群并对其进行研究。首先由定义得到n-正规化子群的一些基本性质。其次,对于任意的正整数n证明了n-正规化子群的存在性。再次,证明了对于有限群G,若# Norm(G)≤3,则G为幂零群;若假定|G|为奇数,则当# Norm(G)≤4时G为幂零群。最后,证明了若# Norm(G)=2,则G″=1;若# Norm(G)=3且G有交换的Sylow2-子群,则G'=1。
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关 键 词: | 有限群 n-正规化子群 幂零群 导列长 |
Finite n-Normalizer Groups |
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Authors: | LIU Yanjun ZHU Yixin School of Mathematical Sciences Peking University Beijing School of Mathematical Sciences Capital Normal University Beijing |
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Institution: | LIU Yanjun 1,ZHU Yixin 2 1School of Mathematical Sciences,Peking University,Beijing 100871, 2School of Mathematical Sciences,Capital Normal University,Beijing 100037, |
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Abstract: | |
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Keywords: | finite groups n-normalizer groups nilpotency derived length |
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