Epimorphisms preserving perfect radicals

Abstract

AbstractThis is an investigation of whether a group epimorphism maps the maximal perfect subgroup of its domain onto that of its image. It is shown how the question arises naturally from considerations of algebraic K-theory and Quillen's plus-construction. Some sufficient conditions are obtained; these relate to the upper central series, or alternatively the derived series, of the domain. By means of topological/homological techniques, the results are then sharpened to provide, in certain circumstances, conditions which are necessary as well as sufficient.