Abstract
We show the finite metacyclic groups G(p,q) admit a class of projective resolutions which are periodic of period 2q and which in addition possess the properties that a) the differentials are 2×2diagonal matrices; b) the Swan–Wall finiteness obstruction (cf. [19,20]) vanishes. We obtain thereby a purely algebraic proof of Petrie's Theorem ([14]) that G(p,q) has free period 2q.
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