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The use of homological techniques in the study of Bass’ conjecture on the Hattori–Stallings rank of finitely generated projective modules over a group ring [1] was pioneered by Eckmann [4]. Working in that direction, we study in this paper a homological condition on a group that takes into account the arithmetic of the coefficient ring and implies the validity of Bass’ conjecture. We also study some properties of the resulting class of groups.