Two classifications of simple Mackey functors with applications to group cohomology and the decomposition of classifying spaces

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)265-304
Number of pages40
JournalJournal of Pure and Applied Algebra
Volume88
Issue number1-3
DOIs
StatePublished - Aug 25 1993

Bibliographical note

Funding Information:
Correspondence to: Professor P. Webb, School of Mathematics, neapolis, MN 55455, USA. Email: webb@math.umn.edu. * Partially supported by the NSF.

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