Two classifications of simple Mackey functors with applications to group cohomology and the decomposition of classifying spaces
Two classifications of simple Mackey functors with applications to group cohomology and the decomposition of classifying spaces
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简单 Mackey 函子的两种分类及其在群上同调和分类空间分解中的应用
DOI：
10.1016/0022-4049(93)90030-w
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发表时间：
1993
影响因子：
0.8
通讯作者：
P. Webb
中科院分区：
文献类型：
--
作者：
P. Webb
给出了有限群的群上同调（具有平凡系数）的一种计算方法，并给出了关于bg稳定分裂的benson - feshach和Martino-Priddy定理的一个新的证明。在这两种情况下，该方法都以一种关键的方式使用了麦基函子的结构性质：我们考虑了简单函子、麦基函子的复合级数和简单麦基函子的投影覆盖。计算群上同调的一个特点是可以同时得到所有有限群与给定sylowp -子群的上同调的-部。
We describe a method of computing the group cohomology (with trivial coefficients) of finite groups, and also give a new proof of a theorem of Benson-Feshbach and Martino-Priddy on the stable splitting ofBG. In both cases the approach uses structural properties of Mackey functors in a crucial way: we consider the simple functors, composition series of Mackey functors, and projective covers of the simple Mackey functors. A feature of the method for computing group cohomology is that one obtains simultaneously thep-part of the cohomology of all finite groups with a given Sylowp-subgroup.