The generating hypothesis for the stable module category of a $p$-group

Details The generating hypothesis for the stable module category of a $p$-group The generating hypothesis for the stable module category of a $p$-group

2006-11-13

arxiv.org/abs/math/0611403v3

Journal of Algebra 310 (2007) 428-433

Mathematics

Representation Theory

6 pages, fixed minor typos, to appear in J. Algebra

Scientific paper

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.

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