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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
Keywords and Phrases:
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