David J. Benson, Sunil K. Chebolu, J. Daniel Christensen, and Jan Minac: The generating hypothesis for the stable module category of a p-group

\/b\e/n\s/o\n/d\j/\ (without the slashes) at maths dot abdn dot ac dot uk, schebolu@uwo.ca, jdc@uwo.ca, and minac@uwo.ca

Submission: 2007, Jan 19

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.

2000 Mathematics Subject Classification: Primary 20C20, 20J06; Secondary 55P42

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