ABSTRACT
Chapter 12. Solvable Groups: W hat Could Be Simpler?
Certain groups are considerably more general than Abelian groups, but possess some of their nice properties. We shall discuss these groups now, in preparation for an application in Chapter 26. The underyling question is, “How far is a given group from being Abelian?” The answer lies in the rather trivial fact that ab = ba iff aba~lb~x = e, which we needed in Proposition 6.13. This leads us to view the subset of elements of the form aba~1 b~ 1 as the obstuction to a group being Abelian.
