The group of endo-permutation modules

Stratifications and Mackey Functors II: Globally Defined Mackey Functors

“…In [32] they were used to give a method for computing group cohomology, and also a new proof of the theorem of Benson-Feshbach and Martino-Priddy on stable decomposition of classifying spaces of finite groups. In [12,9] they were used in a fundamental way in the determination of the Dade group of endopermutation modules. In [10,11] applications were made in which the group of units in the Burnside ring is determined, and in which a description is given of the G-sets which give isomorphic rational representations.…”

The Dade group of a fusion system

“…If j is the inclusion morphism of a subgroup Q of P we write Res P Q instead of Res j . We refer the reader to [7] for more background material and other usual notation concerning the Dade group. In particular, a section of a finite p-group P is a pair ðT; SÞ of subgroups of P such that S t T c P. If R c S t T c P, with R t P, we write In order to describe DðP; FÞ as subgroup of DðPÞ, we use the following terminology.…”

Endo-permutation modules arising from the action of a p-group on a defect zero block

“…Our choice of N implies that G=N is a minimal normal subgroup of G=N z P. Therefore, G=N is a direct product of isomorphic simple groups. The direct product can be eliminated using the fact, which can be found in [1], that Ten P Q ðEnd k ðMÞÞ G End k ðTen P Q ðMÞÞ. Now assume that G is a central p 0 -extension of a simple group.…”