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.
|Number of pages||6|
|Journal||Journal of Algebra|
|Early online date||4 Jan 2007|
|Publication status||Published - 1 Apr 2007|
- generating hypothesis
- stable module category
- ghost map