2020/07/09 by Benson, David J., Carlson, Jon F.
#20C20 #20J06 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2007.04647
Let k be a field of characteristic p > 0. For G an elementary abelian p-group, there exist collections of permutation module such that if C^* is any exact bounded complex whose terms are sums of copies of modules from the collection, then C^* is contractible. A consequence is that if G is any finite group whose Sylow p-subgroups are not cyclic or quaternion, and if C^* is a bounded exact complex such that each Ci is direct sum of one dimensional modules and projective modules, then C^* is contractible.