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We construct groups G that are virtually torsion-free and have virtualcohomological dimension strictly less than the minimal dimension for any modelfor the classifying space for proper actions of G. They are the first examplesthat have these properties and also admit cocompact models for this classifyingspace. We exhibit groups G whose virtual cohomological dimension and Bredoncohomological dimension are two that do not admit any 2-dimensionalcontractible proper G-CW-complex.

On dimensions of groups with cocompact classifying spaces for proper actions