Mappings, homomorphisms, and extensions

Remark If you have not yet done so, read the first part of Section 1.5.2, including eqs. (1.5.5)—(1.5.7), as this constitutes the first part of this section. 

A subset K c G that is the fiber of E in G is called the kernel of the homomorphism. If there is a homomorphism of G on to G (/(G) = G ) of which K is the kernel, with g = kg, so that all fibers of the elements of G (images in the homomorphism) have the same order, then G is called an extension of G by K. An example of an extension is illustrated in Table 1.6 for the particular case of k= 3. 

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