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https://doi.org/10.1016/j.jalgebra.2010.05.009
| Title: | The acyclic group dichotomy | Authors: | Berrick, A.J. | Keywords: | Acyclic group Bass conjecture Baum-Connes conjecture Binate group Cohomological dimension Farkas conjecture Frattini embedding Hattori-Stallings trace Perfect group Primary Secondary |
Issue Date: | 15-Jan-2011 | Citation: | Berrick, A.J. (2011-01-15). The acyclic group dichotomy. Journal of Algebra 326 (1) : 47-58. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jalgebra.2010.05.009 | Abstract: | 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. © 2010 Elsevier Inc. | Source Title: | Journal of Algebra | URI: | http://scholarbank.nus.edu.sg/handle/10635/104248 | ISSN: | 00218693 | DOI: | 10.1016/j.jalgebra.2010.05.009 |
| Appears in Collections: | Staff Publications |
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