| 引用本文： |
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黄琼,韦华全,杨立英,张晓荟.次正规嵌入子群与有限群的p-幂零性[J].广西科学,2011,18(4):325-328. [点击复制]
- HUANG Qiong,WEI Hua-quan,YANG Li-ying,ZHANG Xiao-hui.Subnormally Embedded Subgroups and p-nilpotency of Finite Groups[J].Guangxi Sciences,2011,18(4):325-328. [点击复制]
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| 摘要: |
| 在P是群G的Sylowp-子群,其中p是|G|的一个素因子的条件下,证明G为p-幂零群当且仅当NG (P)为p-幂零群且下列条件之一成立:P的每个极大子群都在G中次正规嵌入;P的每个2-极大子群都在G中次正规嵌入. |
| 关键词: 有限群 p-幂零群 次正规嵌入子群 Sylow子群 极大子群 |
| DOI： |
| 投稿时间：2011-06-27 |
| 基金项目:国家自然科学基金项目(10961007);广西自然科学基金项目(0991101,0991102);广西教育厅科研基金项目资助 |
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| Subnormally Embedded Subgroups and p-nilpotency of Finite Groups |
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HUANG Qiong, WEI Hua-quan, YANG Li-ying, ZHANG Xiao-hui
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| (School of Mathematical Science, Guangxi Teachers Education University, Nanning, Guangxi, 530023, China) |
| Abstract: |
| Let p be a Sylow p-subgroup of a group G, where p is a prime divisor of the order of G.Then G is p-nilpotent if and only if NG (p) is p-nilpotent and one of the following conditions holds:(1) every maximal subgroup of p is subnormally embedded in G; (2) every 2-maximal subgroup of p is subnormally embedded in G. |
| Key words: finite group p-nilpotent group subnormally embedded subgroup Sylow subgroup maximal subgroup |
