turkmath.org

A ghost in the stable module category of a finite group G is a map betweenmodular representations of G, which induces a trivial map on Tate cohomology. The Freyd’s generating hypothesis (GH) for the stable module category of G is the statement that all ghosts between finitely generated modular representations of G 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. We give some new results about some conjectures on the ghost number of mod-p group algebras. This is a joint work with David J. Green