We remark that a very short proof of an elementary result concerning cohomological periods is implicit in the existing literature. As a corollary we show that given a finitely generated stably free resolution of the integers over a finite group, two of its modules are free.
W.H. Mannan. "Periodic cohomology." Homology Homotopy Appl. 10 (2) 135 - 137, 2008.