Homomorphisms

Abstract

The natural maps, called Homomorphisms (and Isomorphisms when the map is a bijection), and factor groups are introduced, and the four fundamental Isomorphism and Correspondence Theorems are derived. Cyclic groups and the basic properties of the automorphism group of a group are described. There are two Web Sections 4.6 and 4.7. The first introduces the ‘transfer’ which provides a useful example of a ‘real’ homomorphism, and the second completes the work on group presentations begun in Chapter 3.