AUTOMORPHISMS OF PRO-p GROUPS OF FINITE VIRTUAL COHOMOLOGICAL DIMENSION

摘要

Let 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.