POST-CLASSIFICATION VERSION OF JORDAN THEOREM ON FINITE LINEAR-GROUPS
POST-CLASSIFICATION VERSION OF JORDAN THEOREM ON FINITE LINEAR-GROUPS
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DOI：
10.1073/pnas.81.16.5278
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发表时间：
1984-01-01
期刊：
影响因子：
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通讯作者：
WEISFEILER, B
中科院分区：
文献类型：
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作者：
WEISFEILER, B
利用有限单群的分类，证明了GLn（C）的有限子群G（其中C为复数）包含一个指数至多为（n+ 1）的交换正规子群M！nalogn+B.此外，如果G是本原的，并且不包含是大交错群的直积的正规子群，则因子（n+ 1）！都可以放弃我进一步证明，如果M是特征p的李型群通过具有可交换ep '-商的正规p-子群的可解群的扩张，则类似的陈述在特征p ≥ 2中也成立。这些结果改进了著名的定理约旦和布劳尔和Feit。
Using classification of finite simple groups, I show that a finite subgroupGof GLn(C), where C = the complex numbers, contains a commutative normal subgroupMof index at most (n+ 1)!nalogn+b. Moreover, ifGis primitive and does not contain normal subgroups that are direct products of large alternating groups, then the factor (n+ 1)! can be dropped. I further show that similar statements hold also in characteristicsp≥ 2, if one takesMto be an extension of a group of Lie type of characteristicpby a solvable group that has a normalp-subgroup with commutativep′-quotient. These results improve the celebrated theorems of Jordan and of Brauer and Feit.