Jonathan Cornick and Ian J. Leary Some remarks concerning degree zero complete cohomology Abstract. We describe degree zero mod-p complete cohomology modulo its radical in purely group-theoretic terms, for members of a class of groups that includes all groups of finite virtual cohomological dimension. We give examples to show that our description does not apply to all discrete groups. We also give examples of discrete groups that are not 'Quillen groups' in the sense of H.-W. Henn.