Extensions and Cohomology
Among the subjects we shall touch upon in this chapter there is that of extensions. We have already mentioned this problem in Chapter 2 when talking about Höolder’s program for the classification of finite groups. As we shall see, the solution proposed by Schreier in the years 1920’s allows a classification of the groups that are extensions of an abelian group A by a group π by means of equivalence classes of functions π×π → A. Unfortunately, one does not obtain a system of invariants for the isomorphism classes of the groups obtained in this way, because nonequivalent functions can yield isomorphic groups. No characterization of the isomorphism classes is known.