Abstract
A discrete group Γ is said to be of type F(n) if and only if there is a classifying complex BΓ with finite n-skeleton. We show that Γ is of type F(n) if Γ admits a regular cellular action on a CW complex Y such that Y is homotopy equivalent to a complex with finite ( n−1)-skeleton, Y Γ is a complex with finite n-skeleton, and for each p-cell σ of Y(0⩽ p⩽ n) the stabilizer Γ σ is of type F(n−p) .
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