Abstract
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 S 1 G , by explicit generators and relations.
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