Lifting endo-trivial modules

Abstract

this paper, we solve the problem in the key case of endo-trivial modules. Let R be a complete discrete valuation ring of characteristic zero with maximal ideal J and residue class field k of prime characteristic p. For a fixed finite p-group P , all the kG-modules considered will be finite dimensional and all the RP-modules will be finitely generated and free as R-modules. An RG-module M (and similarly for RP-modules) is an endo-trivial module if the tensor product M M is the direct sum of the trivial RP-module R and a free RG-module. The standard results of the theory of such modules may be found in the references [4, 5, 8]