| 引用本文： |
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曾凡辉,李世荣.半正规、C-正规对群超可解性的影响[J].广西科学,2003,10(3):161-164,168. [点击复制]
- Zeng Fanhui,Li Shirong.Influence of Semi-Normal Subgroups and C-Normal Subgroups on the Supersolvability of Groups[J].Guangxi Sciences,2003,10(3):161-164,168. [点击复制]
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| 摘要: |
| 利用某些半正规或C-正规子群刻划有限群的结构,得到有限群超可解的若干充分条件:设有限群G=AB,其中A≤G,B≤G.若A与B的所有Sylow子群在G中半正规,则G超可解;设G是有限群,N4G,G/N超可解.若N的所有素数阶子群含于U(G),且N的所有22阶循环子群在G中或半正规或C-正规,则G是超可解群.同时推广了一些已知的结果. |
| 关键词: 半正规 C-正规 超可解 超可解嵌入子群 Sylow基 |
| DOI： |
| 投稿时间：2002-11-26 |
| 基金项目:国家自然科学基金项目(编号10161001)和广西自然科学基金项目资助。 |
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| Influence of Semi-Normal Subgroups and C-Normal Subgroups on the Supersolvability of Groups |
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Zeng Fanhui, Li Shirong
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| (Dept. of Math. & Info. Sci., Guangxi Univ., 100 Daxuelu, Nanning, Guangxi, 530004, China) |
| Abstract: |
| Using semi-normal subgroups and C-normal subgroups to characterize the structure of finite groups,some sufficient conditions for finite groups to be supersolvable of supposing finite groups G=AB,A ≤ G,B ≤ G are obtained.And if all Sylow subgroups of A and B are semi-normality in G,then G is supersolvable;if G is finite group,then N4G,G/N is supersolvable;if all prime subgroups of N include in U(G),and all 22 steppes of circulation subgroup of N are semi-normality or C-normality in group G,then G is supersolvability.Some previously known results are extended. |
| Key words: semi-normality C-normality supersolvable supersolvable embedding subgroups sylow basis |
