Unitals in projective planes

Gary Ebert, Susan Barwick (auth.)0387763643, 9780387763644, 9780387763668

This clearly written text is the first book on unitals embedded in finite projective planes. Unitals are key structures in square order projective planes, and have connections with other structures in algebra. They provide a link between groups and geometries. There is a considerable number of research articles concerning unitals, and there also exist many open problems. This book is a thorough survey of the research literature on embedded unitals which collects this material in book form for the first time. The book is aimed at graduate students and researchers who want to learn about this topic without reading all the original articles.

The primary proof techniques used involve linear algebraic arguments, finite field arithmetic, some elementary number theory, and combinatorial enumeration. Some computer results not previously found in the literature also are mentioned in the text. The authors have included a comprehensive bibliography which will become an invaluable resource.

Gary Ebert is Professor of Mathematics at the University of Delaware, USA. Susan Barwick is a Senior Lecturer of Mathematics at the University of Adelaide, Australia.

Table of contents :
Front Matter….Pages 1-9
Preliminaries….Pages 1-20
Hermitian Curves and Unitals….Pages 1-11
Translation Planes….Pages 1-25
Unitals Embedded in Desarguesian Planes….Pages 1-29
Unitals Embedded in Non-Desarguesian Planes….Pages 1-20
Combinatorial Questions and Associated Configurations….Pages 1-23
Characterization Results….Pages 1-34
Open Problems….Pages 1-3
Back Matter….Pages 1-22