Inclusion P(ZG) ⊂ Cof(ZG) for all groups

Establish that for every group G, the class P(ZG) of ZG-modules that occur as cokernels of acyclic complexes of projective ZG-modules is contained in the class Cof(ZG) of Benson cofibrant ZG-modules, thereby implying Cof(ZG) = GProj(ZG) = P(ZG).

Background

The class P(ZG) consists of modules arising as cokernels of acyclic complexes of projectives; showing P(ZG) ⊂ Cof(ZG) would place these within Benson’s cofibrant class and, together with known inclusions, yield the equality Cof(ZG) = GProj(ZG) = P(ZG).

This conjecture directly connects classical acyclicity with cofibrancy, and its resolution would unify several important classes in Gorenstein homological algebra over group rings with integer coefficients.