Searching for Relations

In this chapter, we establish the presentations that we introduced in Chapter 10. First, though, we must clear up the little matter of “left” and “right.”

If α and β are two group operations, what should αβ mean? Many mathematicians write α(P ) for the image of P under α, which has the rather confusing effect that αβ means “β, followed by α”. In this book, we adopt the more natural meaning “α followed by β” and so write Pα for the image of P under α.