1. CMB 2011 (vol 55 pp. 48)
||Freyd's Generating Hypothesis for Groups with Periodic Cohomology|
Let $G$ be a finite group, and let $k$ be a field whose characteristic $p$
the order of $G$.
Freyd's generating hypothesis for the stable module category of
$G$ is the statement that a map between finite-dimensional
$kG$-modules in the thick subcategory generated by $k$ factors through a
projective if the induced map on Tate cohomology is trivial. We show that if
has periodic cohomology, then the generating hypothesis holds if and only if
$p$-subgroup of $G$ is $C_2$ or $C_3$. We also give some other conditions
that are equivalent to the GH
for groups with periodic cohomology.
Keywords:Tate cohomology, generating hypothesis, stable module category, ghost map, principal block, thick subcategory, periodic cohomology
Categories:20C20, 20J06, 55P42