On the lifting of the Dade group

Abstract

For the group of endo-permutation modules of a finite $p$-group, there is a surjective reduction modulo $p$ homomorphism from a complete discrete valuation ring of characteristic 0 to its residue field of characteristic $p$. We prove that this reduction map always has a section which is a group homomorphism.Comment: V2: capped endo-permutation modules were replaced by strongly capped endo-permutation module