turkmath.org

A ghost in the stable module category of a finite group G is a map between modular representations of G, which induces a trivial map on Tate cohomology. The Fredy's generating hypothesis (GH) for the stable module category of G is the statement that all ghosts between finitely generated kG-modules factor through a projective kG-module. For most p-groups GH fails and the ghost number of the group algebra kG is defined as an invariant which measures the degree of the failure of GH. Christensen and Wang give conjectural upper and lower bounds for the ghost number of the group algebra of a p-group. We prove the conjecture for most p-groups. We also prove Wang's conjecture on the ghost number of the group algebra of the quaternion group of order eight. This is a joint work with David J. Green.