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On calcule dans cet article l’homologie stable des groupes orthogonaux et symplectiques sur un corps fini à coefficients tordus par un endofoncteur usuel des -espaces vectoriels (puissance extérieure, symétrique, divisée...). Par homologie stable, on entend, pour tout entier naturel , les colimites des espaces vectoriels et — dans cette situation, la stabilisation (avec une borne explicite en fonction de et ) est un résultat classique de Charney.
Tout d’abord, nous donnons un cadre...
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here “compute” means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet).Next,...
Let X be a p-compact group, with maximal torus BT → BX, maximal torus normalizer BN and Weyl group . We prove that for an odd prime p, the fibration has a section, which is unique up to vertical homotopy.
We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated...
We prove vanishing results for the unramified stable cohomology of alternating groups.
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