COTORSION DIMENSIONS OVER GROUP RINGS

Let Γ be a group, Γ′ a subgroup of Γ with finite index and M be a Γ-module. We show that M is cotorsion if and only if it is cotorsion as a Γ′-module. Using this result, we prove that the global cotorsion dimensions of rings ZΓ and ZΓ′ are equal.