Translation Planes - Lüneburg, Heinz 1935-2009 (Springer Berlin Heidelberg, 1980)
Wir unterhielten uns einmal darüber, daß man sich in einer fremden Sprache nur unfrei ausdrücken kann und im Zweifelsfall lieber das sagt, was man richtig und einwandfrei zu sagen hofft, als das, was man eigentlich sagen will. Molnar nickte bestätigend: "Es ist sehr traurig", resümierte er. "Ich habe oft mitten im Satz meine Weltanschauung ändern müssen . . . " Friedrich Torberg, Die Tante Jolesch The last two decades have witnessed great progress in the theory of translation planes. Being interested in, and having worked a little on this subject, I felt the need to clarify for myself what had been happening in this area of mathematics. Thus I lectured about it for several semesters and, at the same time, I wrote what is now this book. It is my very personal view of the story, which means that I selected mainly those topics I had touched upon in my own investigations. Thus finite translation planes are the main themes of the book. Infinite translation planes, however, are not completely disregarded. As all theory aims at the mastering of the examples, these play a central role in this book. I believe that this fact will be welcomed by many people. However, it is not a beginner's book of geometry. It presupposes considerable knowledge of projective planes and algebra, especially group theory. The books by Gorenstein, Hughes and Piper, Huppert, Passman, and Pickert mentioned in the bibliography will help to fill any gaps the reader may have