ABSTRACT
In this chapter, we will be concerned with the following kinds of problems: (1) Given groups A, G, when is there a group C such that C contains a normal subgroup A′ ≅ A and such that the factor group C/A′ ≅ G? Such a group C is (loosely) called an extension of A by G. A more precise definition of extension will follow. (2) If there is such a C, what can we say about its structure? (The group C is certainly not always completely determined; S 3 and Z(6) are both extensions of Z(3) ≅ A 3 by Z(2).)
