The Acyclic Group Dichotomy
نویسنده
چکیده
Two extremal classes of acyclic groups are discussed. For an arbitrary group G, there is always a homomorphism from an acyclic group of cohomological dimension 2 onto the maximum perfect subgroup of G, and there is always an embedding of G in a binate (hence acyclic) group. In the other direction, there are no nontrivial homomorphisms from binate groups to groups of nite cohomological dimension. Binate groups are shown to be of signi cance in relation to a number of important K-theoretic isomorphism conjectures.
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