| 次正规嵌入子群与有限群的可解性（Ⅰ） |
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| 引用本文： | 杨立英,韦华全,黄琼,钟国,马儇龙.次正规嵌入子群与有限群的可解性（Ⅰ）[J].广西师院学报,2013(4):18-21. |
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| 作者姓名： | 杨立英 韦华全 黄琼 钟国 马儇龙 |
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| 作者单位： | 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（10961007,11161006）;广西自然科学基金（0991102,0991101）;广西教育厅科研基金 |
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| 摘 要： | 证明了，设 P是群G的Sylow 2-子群，若 P的极大子群都在G中次正规嵌入，则 G可解；若群 G的Sylow 2-子群的循环子群均在G中次正规嵌入，则G可解；设M为群G的幂零极大子群或M为群G的内2-幂零极大子群，若 M的Sylow 2-子群的极大子群都在G中次正规嵌入，则G可解。
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| 关 键 词： | 可解群 次正规嵌入子群 Sylow 2-子群 极大子群 循环子群 |
Subnormally Embedded Subgroups and Solvability of Finite Groups |
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| YANG Li-ying,WEI Hua-quan,HUANG Qiong,ZHONG Guo,MA Xuan-long.Subnormally Embedded Subgroups and Solvability of Finite Groups[J].Journal of Guangxi Teachers College(Natural Science Edition),2013(4):18-21. |
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| Authors: | YANG Li-ying WEI Hua-quan HUANG Qiong ZHONG Guo MA Xuan-long |
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| Institution: | (School of Mathematical Science,Guangxi Teachers Education University,Nanning 530023, China) |
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| Abstract: | Let P be a Sylow 2-subgroup of a group G I.f the maximal subgroup of P is subnormal-ly embedded in G ,then G is solvable I.f a cyclic subgroup of Sylow 2-subgroup of a group G is subnor-mally embedded in G .then G is solvable .Let M be a nilpotnent maximal subgroup of a group G or M be an inner 2-nilpotent maximal subgroup of a group G ,if the maximal subgroup of Sylow 2-subgroup of M is subnormally embedded in G ,then G is solvable . |
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| Keywords: | solvoble group subnormally embedded subgroup Sylow 2-subgroup maximal sub-group cyclic subgroup |
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