Automorphisms of Finite Groups pp 29-67 | Cite as

# Fundamental Exact Sequence of Wells

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## 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.

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