| 两种子群特性与有限群的超可解性 |
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| 引用本文： | 石向东,韦华全,谢芬芳.两种子群特性与有限群的超可解性[J].广西师范学院学报(自然科学版),2012,29(1):5-8. |
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| 作者姓名： | 石向东 韦华全 谢芬芳 |
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| 作者单位： | 1. 梧州学院数理系,广西梧州,543002
2. 广西师范学院数学科学学院,广西南宁,530023 |
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| 基金项目： | 国家自然科学基金，广西自然科学基金，广西教育厅科研基金 |
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| 摘 要： | 证明了：（1）设G是有限p-可解群,P∈Sylp（G）,则G是p-超可解当且仅当P的极大子群在G中半覆盖-远离或G-半置换.（2）有限群G为超可解当且仅当对于G的每个素因子p,存在P∈Sylp（G）使得P的极大子群都在G中半覆盖-远离或PFp（G）-半置换.（3）设F是包含超可解群系的饱和群系,G是有限群,H G使得G/H∈F.如果对于H的任意素因子p,存在P∈Sylp（H）使得P的极大子群都在G中半覆盖-远离或PFp（H）-半置换,则G∈F.
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| 关 键 词： | 有限群 超可解群 半覆盖-远离子群 X-置换 饱和群系 |
Two Characteristics of Subgroups and the Supersolvability of Finite Groups |
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| SHI Xiang-dong,WEI Hua-quan,XIE Fen-fang.Two Characteristics of Subgroups and the Supersolvability of Finite Groups[J].Journal of Guangxi Teachers Education University:Natural Science Edition,2012,29(1):5-8. |
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| Authors: | SHI Xiang-dong WEI Hua-quan XIE Fen-fang |
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| Institution: | 1.Department of Mathematics and Physics,Wuzhou College,Wuzhou 543002,P.R.China;2.School of Mathematical Sciences,Guangxi Teachers Education University,Nanning 530023,P.R.China) |
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| Abstract: | The following results were proved:(1) Let G be finite p-solvable group and let P∈Sylp(G).Then G is p-supersolvable if and only if every maximal subgroup of P is either semi-cover-avoiding or G-semipermutable in G.(2) A finite groups is supersolvable if and only if for every prime divisor of |G|,there exists P∈Sylp(G) such that every maximal subgroup of P is either semi-cover-avoiding or PFp(G)-semipermutable in G.(3) Let F be a saturated formation containing the class of supersolvable groups,G a finite group and H■G such that G/H∈F.If for every prime divisor of |H|,there exists P∈Sylp(H) such thatevery maximal subgroup of P is either semi-cover-avoiding or PFp(H)-semipermutable in G,then G∈F. |
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| Keywords: | finite group supersolvable group semi-cover-avoiding subgroup X-semipermutable subgroup saturated formation |
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