An important tool in the analysis of discrete groups of finite virtual cohomological dimension is the existence of a finite dimensional contractible CW-complex on which the group acts with finite stabilizers. We develop a purely algebraic analogue for profinite groups. This enables us to reveal the connection between finiteness conditions on the cohomology of the group and those on the normalizers of the finite p-subgroups.
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Peter Symonds, Permutation complexes for profinite groups. Comment. Math. Helv. 82 (2007), no. 1, pp. 1–37DOI 10.4171/CMH/83