Natural maps of extension functors and a theorem of R. G. Swan

The present paper has been inspired by a theorem of Swan(5). The theorem can be described as follows. Let G be a finite group and let Γ be its integral group ring. We shall denote by Z an infinite cyclic additive group considered as a left Γ-module by defining gm = m for all g in G and m in Z . By a Tate resolution of Z is meant an exact sequence where X n is a projective module for − ∞ < n < + ∞, and .