The Mod 2 Cohomology Rings of Rank 3 Simple Groups are Cohen – Macaulay
The Mod 2 Cohomology Rings of Rank 3 Simple Groups are Cohen – Macaulay
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3 阶简单群的 Mod 2 上同调环是 Cohen –Macaulay
DOI：
10.1515/9781400882588-004
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
A. Adem
中科院分区：
文献类型：
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作者：
A. Adem
近年来，我们一直在研究散在单群的上同调环及其与代数和同伦理论中问题的关系。（K是特征p的域）与G的模表示的结构的关系，以及有限群论与稳定同伦理论通过标识B + S ∞ Q（S 0）的联系.有限群G的秩（或2-秩）是G中包含的最大2-初等子群（Z/2）m的维数，这至少在低秩时提供了一种组织单群的方便方法。唯一秩为1的单群是Z/2。对于秩为2的单群，分类由以下定理给出，由于（我们在§1中回顾这些分类结果）。在这个列表中，当特征q为奇数时，Lie型群的mod（2）上同调与分类空间B G的上同调紧密相连，其中G
In recent years we have been studying the cohomology rings of the sporadic simple groups and their relations with problems in algebra and homotopy theory. (K a field of characteristic p) with the structure of modular representations of G, and also by the connection of finite group theory with stable homotopy theory through the identification B + S ∞ ≃ Q(S 0). The rank (or 2-rank) of a finite group G is the dimension of the largest 2-elementary subgroup (Z/2) m contained in G, and this provides, at least in low rank, a convenient method for organizing the simple groups. The only simple group of rank 1 is Z/2. For the simple groups of rank two the classification is given by the following theorem due to (We review these classification results in §1.) In this list, the mod(2) cohomology of the groups of Lie type when the characteristic q is odd are closely tied to the cohomology of the classifying space B G , where G