Michel Broué

Equivalences of Blocks of Group Algebras

Let O be a complete local noetherian ring, whose field of fractions has characteristic zero and residue field has non-zero characteristic. A block algebra over O is an indecomposable summand of the algebra of a finite group over O.

Characters and local structure in G-algebras

Let p be a prime number and let G be a finite group. Let x be a generalized character in ap-block b of G. If P is a Sylowp-subgroup of G and T] is a generalized character of P such that T(X) = v then, we set

Isométries de caractères et équivalences de Morita ou dérivées

© Publications mathématiques de l’I.H.É.S., 1990, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). 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.

Remarks on blocks and subgroups

Abstract The aim of this paper is to present simple methods to study certain relations between the p -blocks of a finite group G and the p -blocks of a subgroup H of G . By using these tools, we can find some properties of the “Brauer correspondence” of blocks, and generalize in a simple way some results of Isaacs and Scott [2].