Abstract
AbstractLet G be a pro-p group of finite cohomological dimension and type FP ∞ and T be a finite p-group of automorphisms of G. We prove that the group of fixed points of T in G is again a pro-p group of type FP ∞ (in particular it is finitely presented). Moreover, we prove that a pro-p group G of type FP ∞ and finite virtual cohomological dimension has finitely many conjugacy classes of finite subgroups.
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