Structure locale dans les groupes finis

Abstract

Structure locale dans les groupes finis Mémoires de la S. M. F., tome 47 (1976) <http://www.numdam.org/item?id=MSMF_1976__47__5_0> © Mémoires de la S. M. F., 1976, tous droits réservés. L'accès aux archives de la revue « Mémoires de la S. M. F. » (http://smf. emath.fr/Publications/Memoires/Presentation.html) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Frobenius categories

“…3. The existence of the localizing functor over the Brauer category of a blockproved in [10]-pushed us to look for an abstract description which could allow an eventual classification of the "p-local structures," a purpose already hazarded in [8]. From this spirit, in 1991 we found the Frobenius categories over a finite p-group; our work, widely presented in Chevalley's Seminar, remained unpublished waiting for a significant test on its interest.…”

“…Let p be a prime number and G a finite group; since [8] we try to understand the meaning of what was vaguely called "p-local structure of G" and, on this way, in our Bourbaki's lecture [9] we formally introduced the Frobenius category of G (at p)-namely, the category F G formed by all the p-subgroups of G, and all the group homomorphisms between them induced by the inner automorphisms of G and by their inclusions-a usual terminology in Chevalley's Seminar. The fundamental Frobenius' Criterion on the existence of a normal p-complement in G can be viewed as the conceptual origin of this approach.…”

Almost All Generalized Extraspecial p-Groups Are Resistant

“…For a Sylow p-subgroup P of G, Alperin showed in [Al] that these morphisms are locally controlled, i.e., by normalizers N G Q for Q a subgroup of P. Nine years later, Puig [Pu1] refined this and required Q to be an essential p-subgroup of G. In what follows, we will give the definition and some basic properties of essential p-subgroups of G.…”

The Dade group of a fusion system

“…We review the definition of a fusion system, a concept due to Puig [19]. Our terminology follows [2] or [17].…”