Composition Factors from the Group Ring and Artin's Theorem on Orders of Simple Groups
Composition Factors from the Group Ring and Artin's Theorem on Orders of Simple Groups
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DOI：
10.1112/plms/s3-60.1.89
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发表时间：
1990
影响因子：
1.8
通讯作者：
W. Kimmerle;R. Lyons;R. Sandling;David N. Teague
中科院分区：
文献类型：
--
作者：
W. Kimmerle;R. Lyons;R. Sandling;David N. Teague
有限群的整群环决定了群主因子的同构类型。给出了两个证明，其中一个证明将Cameron和Teague关于有限单群阶的Artin定理的推广应用于特征单群阶。这种推广表明，有限单群的直接幂是由它的阶决定的，但也有两种例外。这里详细地给出了它的证明，对马丁隐式使用的某些自然数变量的函数进行了改编和显式的证明。这些函数通过一系列提供有限单群阶的值的表来提供实参。
The integral group ring of a finite group determines the isomorphism type of the chief factors of the group. Two proofs are given, one of which applies Cameron's and Teague's generalisation of Artin's theorem on the orders of finite simple groups to the orders of characteristically simple groups. The generalisation states that a direct power of a finite simple group is determined by its order with the same two types of exception which Artin found. Its proof, given here in detail, adapts and makes explicit certain functions of a natural number variable which Artin used implicitly. These functions contribute to the argument through a series of tables which supply their values for the orders of finite simple groups.