2009/01/20 by Bouc, Serge
#16P90 #18G10 #18G15 #20J05 #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.0901.3090
Let k be a field of characteristic p>0. Call a finite group G a poco group over k if any finitely generated cohomological Mackey functor for G over k has polynomial growth. The main result of this paper is that G is a poco group over k if and only if the Sylow p-subgroups of G are cyclic, when p>2, or have sectional rank at most 2, when p=2. A major step in the proof is the case where G is an elementary abelian p-group. In particular, when p=2, all the extension groups between simple functors can be determined completely, using a presentation of the graded algebra of self extensions of the simple functor S1G, by explicit generators and relations.