no. 4
Group theory
A new canonical induction formula for p-permutation modules
[Une nouvelle formule d'induction canonique pour modules de p-permutation]

Présenté par : the Editorial Board

Barker, Laurence1 ; Mutlu, Hatice1
1 Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey
Comptes Rendus. Mathématique, Tome 357 (2019) no. 4, pp. 327-332.

En application de la théorie de l'induction canonique de Robert Boltje, nous présentons une formule stable par restriction au moyen de laquelle tout module de p-permutation est exprimé sous forme de combinaison Z[1/p]-linéaire des inductions des inflations des modules projectifs associés à des groupes de sous-quotients. Les constructions concernées comprennent, pour tout groupe fini, un anneau qui a une Z-base indexée par les classes de conjugaison des triplets (U,K,E) avec U un sous-groupe, Op′(K)=K⊴U et E un module projectif indécomposable de l'algèbre de groupe de U/K.

Applying Robert Boltje's theory of canonical induction, we give a restriction-preserving formula expressing any p-permutation module as a Z[1/p]-linear combination of modules induced and inflated from projective modules associated with subquotient groups. The underlying constructions include, for any given finite group, a ring with a Z-basis indexed by conjugacy classes of triples (U,K,E) where U is a subgroup, K is a p′-residue-free normal subgroup of U, and E is an indecomposable projective module of the group algebra of U/K.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.04.004
Barker, Laurence 1 ; Mutlu, Hatice 1

1 Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey 
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Barker, Laurence; Mutlu, Hatice. A new canonical induction formula for p-permutation modules. Comptes Rendus. Mathématique, Tome 357 (2019) no. 4, pp. 327-332. doi : 10.1016/j.crma.2019.04.004. http://www.numdam.org/articles/10.1016/j.crma.2019.04.004/

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