A new canonical induction formula for p-permutation modules [Une nouvelle formule d'induction canonique pour modules de p-permutation]

Abstract

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.