Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd's generating hypothesis holds for a non-trivial finite p-group G if and only if G is either C2 or C3. We also give various conditions which are equivalent to the generating hypothesis. © 2007 Elsevier Inc. All rights reserved.
Benson, D. J., Chebolu, S. K., Christensen, J. D., & Mináč, J. (2007). The generating hypothesis for the stable module category of a p-group. Journal of Algebra, 310(1), 428–433. https://doi.org/10.1016/j.jalgebra.2006.12.013