q-Clan Geometries in Characteristic 2 [electronic resource] / by Ilaria Cardinali, Stanley E. Payne.

q-Clans and Their Geometries -- The Fundamental Theorem -- Aut(GQ(C)) -- The Cyclic q-Clans -- Applications to the Known Cyclic q-Clans -- The Subiaco Oval Stabilizers -- The Adelaide Oval Stabilizers -- The Payne q-Clans -- Other Good Stuff.

This monograph offers the only comprehensive, coherent treatment of the theory - in characteristic 2 - of the so-called flock quadrangles, i.e., those generalized quadrangles (GQ) that arise from q-clans, along with their associated ovals. Special attention is given to the determination of the complete oval stabilizers of each of the ovals associated with a flock GQ. A concise but logically complete introduction to the basic ideas is given. The theory of these flock GQ has evolved over the past two decades and has reached a level of maturation that makes it possible for the first time to give a satisfactory, unified treatment of all the known examples. The book will be a useful resource for all researchers working in the field of finite geometry, especially those interested in finite generalized quadrangles. It is of particular interest to those studying ovals in finite Desarguesian planes.