Freyd's generating hypothesis for groups with periodic cohomology, by Sunil K. Chebolu, J. Daniel Christensen, and Jan Minac

Let G be a finite group and let k be a field whose characteristic p divides the order of G. Freyd's generating hypothesis for the stable module category of G is the statement that a map between finite-dimensional kG-modules in the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. We show that if G has periodic cohomology then the generating hypothesis holds if and only if the Sylow p-subgroup of G is C_2 or C_3. We also give some other conditions that are equivalent to the GH for groups with periodic cohomology.

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