Embeddings into k-Efficient Groups

Abstract

We prove a theorem with the following corollary: For each integer k ≥ 1, an arbitrary finite group G embeds into some finite group G k for which there exists an Eilenberg-Mac Lane CW-space X = K G k 1 whose finite n-skeleton X n has Euler-Poincaré characteristic χ X n = 1 + −1 n dH n G k for all n ≤ k. The theorem can be viewed as a generalisation of a result of J. Harlander [1996, J. Algebra 182, 511-521] on the embedding of finite groups into groups with "efficient" presentations. 