Freyd's Generating Hypothesis for Groups with Periodic Cohomology
2012 ◽
Vol 55
(1)
◽
pp. 48-59
◽
Keyword(s):
AbstractLet G be a finite group, and let k be a field whose characteristic p divides 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 G has periodic cohomology, then the generating hypothesis holds if and only if the Sylow p-subgroup of G is C2 or C3. We also give some other conditions that are equivalent to the GH for groups with periodic cohomology.
Keyword(s):
2007 ◽
Vol 310
(1)
◽
pp. 428-433
◽
2019 ◽
Vol 155
(2)
◽
pp. 424-453
◽
Keyword(s):
2013 ◽
Vol 11
(2)
◽
pp. 297-329
◽
2016 ◽
Vol 102
(1)
◽
pp. 74-95
1999 ◽
Vol 50
(199)
◽
pp. 355-369
2016 ◽
Vol 68
(2)
◽
pp. 258-279
◽
Keyword(s):
2011 ◽
Vol 8
(3)
◽
pp. 507-542
◽
2012 ◽
Vol 11
(01)
◽
pp. 1250001
◽
Keyword(s):