### The generating hypothesis for the stable module category of a p-group, by David J. Benson, Sunil K. Chebolu, J. Daniel Christensen, and Jan Minac

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 C_2 or C_3. We also give various
conditions which are equivalent to the generating hypothesis.

AMS Subject classsification: Primary 20C20, 20J06; Secondary 55P42

Journal Information: To appear in the Journal of Algebra.

David J. Benson </be/ns/on/dj/ (without the slashes) at maths dot abdn dot ac dot uk>

Sunil K. Chebolu <schebolu@uwo.ca>

J. Daniel Christensen <jdc@uwo.ca>

Jan Minac <minac@uwo.ca>