Title: The generating hypothesis for the stable module category of a p-group
Authors: David J. Benson, Sunil K. Chebolu, J. Daniel Christensen, and
Jan Minac
Email addresses: $\backslash$/b$\backslash$e/n$\backslash$s/o$\backslash$%
n/d$\backslash$j/$\backslash$ (without the slashes) at maths dot
abdn dot ac dot uk, schebolu@uwo.ca, jdc@uwo.ca, and minac@uwo.ca
AMS Subject classsification: Primary 20C20, 20J06; Secondary 55P42
Journal Information: To appear in the Journal of Algebra.
ABSTRACT: 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.
Comments: This replaces an earlier version with filename
GH-pgroup-new.dvi after fixing very minor typos.