TY - JOUR
T1 - Two classifications of simple Mackey functors with applications to group cohomology and the decomposition of classifying spaces
AU - Webb, Peter
N1 - Funding Information:
Correspondence to: Professor P. Webb, School of Mathematics, neapolis, MN 55455, USA. Email: [email protected]. * Partially supported by the NSF.
PY - 1993/8/25
Y1 - 1993/8/25
N2 - 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 of BG. 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 the p-part of the cohomology of all finite groups with a given Sylow p-subgroup.
AB - 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 of BG. 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 the p-part of the cohomology of all finite groups with a given Sylow p-subgroup.
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U2 - 10.1016/0022-4049(93)90030-W
DO - 10.1016/0022-4049(93)90030-W
M3 - Article
AN - SCOPUS:38249000895
SN - 0022-4049
VL - 88
SP - 265
EP - 304
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 1-3
ER -