The acyclic group dichotomy

Details The acyclic group dichotomy The acyclic group dichotomy

2010-06-21

arxiv.org/abs/1006.4009v1

Journal of Algebra (2010)

Mathematics

Group Theory

To appear

Scientific paper

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 finite cohomological dimension. Binate groups are shown to be of significance in relation to a number of important K-theoretic isomorphism conjectures.

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