Lluis Puig

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

Affirmative answer to a question of Feit

As he points out, if P is abelian the affirmative answer follows from Dade’s classification [4]. Our purpose here is to show that the general case reduces to the abelian one, which answers affirmatively Feit’s question. More generally, in [4] Dade determines the cap group associated with a finite abelian p-group showing in particular that this group is finitely generated: our main result here (cf. Theorem 2.2 below) implies that finite generation is still true in the non-abelian case (cf. Corollary 2.4 below). This result and the main steps of a proof were already announced in 17, Section81 and here we are just discharging ourselves of an old debt. Actually, as we said in [7, Section81, our result would follow from a complete classification of endo-permutation modules.

On Blocks with Nilpotent Coefficient Extensions

For modular group algebras over an arbitrary field we define new type of blocks: blocks with nilpotent extensions, and describe their source algebras. To do it, a general pattern is proposed for relations between the source algebra of a block and the source algebra of a block appearing in its decomposition in a suitable extension of the field of coefficients.

Une correspondance de modules pour les blocs à groupes de défaut abéliens

AbstractLet b be a block of a finite group G with an abelian defect group P and an inertial quotient E. Let us denote by L the semi-direct product of P and E. If E is cyclic and acts freely on P−{1}, we prove that the stable categories of

Pointed Groups on the Group Algebra

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Fusion ℤ-algebra of a Block

Gb- and

Local Structure of the Hyperfocal Subalgebra

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