### 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.

Sunil K. Chebolu <schebolu@uwo.ca>

J. Daniel Christensen <jdc@uwo.ca>

Jan Minac <minac@uwo.ca>