Groups with no infinite perfect subgroups and aspherical 2-complexes (Q1311215)

This paper is a further contribution of the author to J. H. C. Whitehead's question whether every subcomplex of an aspherical 2-complex is also aspherical. The main result is that, if \(P\) is a nontrivial, finite, superperfect, normal subgroup of a finitely presented group \(G\) such that \(Q = G/P\) has cohomological dimension 1 or 2, then \(G\) is not \(P\)-Cockroft. As a consequence, Whitehead's question is answered positively, if the fundamental group of the subcomplex has no infinite perfect subgroups. This improves a result of J. F. Adams.