A new canonical induction formula for p-permutation modules

Abstract

Applying Robert Boltje's theory of canonical induction, we give a restrictionpreserving 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. 2010 Mathematics Subject Classification: 20C20.