Approximate finiteness properties of infinite groups

Pt discrete group Gamma is said to be of type F(n) if and only if there is a classifying complex B Gamma with finite n-skeleton. We show that Gamma is of type F(n) if Gamma 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/Gamma is a complex with finite rr-skeleton,and for each p-cell sigma of Y (0 less than or equal to p less than or equal to n) the stabilizer Gamma(sigma), is of type F(n - p). (C) 1998 Elsevier Science Ltd. All rights reserved.