Title: Groups which do not admit ghosts

Authors: Sunil K. Chebolu, J. Daniel Christensen, and Jan Minac

Address: Department of Mathematics 
         University of Western Ontario
         London, ON N6A 5B7, Canada

Email addresses: schebolu@uwo.ca, jdc@uwo.ca, and minac@uwo.ca

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

Journal Information: To appear in the Proceedings of the AMS.

ABSTRACT: A ghost in the stable module category of a group G is a map between
representations of G that is invisible to Tate cohomology. We show that the
only non-trivial finite p-groups whose stable module categories have no 
non-trivial ghosts are the cyclic groups of order 2 and 3. We compare this to 
the situation in the derived category of a commutative ring. We also determine 
for which groups G the second power of the Jacobson radical of kG is stably 
isomorphic to a suspension of k.

Comments: This replaces an earlier version with filename GH-StMod.dvi