Fundamental Exact Sequence of Wells

Abstract

Given a normal subgroup N of a group G, a basic problem in the theory of automorphisms of groups is that of extending an automorphism of N to an automorphism of G, and the analogous one of lifting an automorphism of the quotient group G / N to an automorphism of G. A crucial role in the investigation of these problems is played by an exact sequence due to Wells [126]. In this chapter, a detailed exposition of this sequence and its role in determining conditions for extension and lifting of automorphisms is presented.