ABSTRACT
In this chapter we will introduce solvable groups, as a natural generalization of abelian groups. Solvable groups can be viewed as groups built out of finitely many abelian pieces. This gives us a chance to see a bit of how the extension problem in groups is approached; we discussed these ideas briefly in the historical note at the end of Chapter 34. We will use the notion of solvability in Chapter 49, when we discuss whether a polynomial equation can be solved using ordinary arithmetic and the extraction of roots.
