Orthogonal Latin Squares Based on Groups (eBook)

​Anthony B. Evans is Professor of Mathematics at Wright State University in Dayton, Ohio. Since the mid 1980s, his primary research has been on orthomorphisms and complete mappings of finite groups and their applications. These mappings arise in the study of mutually orthogonal latin squares that are derived from the multiplication tables of finite groups. As an offshoot of this research, he has also worked on graph representations. His previous book, Orthomorphism Graphs of Groups (1992), appeared in the series, Lecture Notes in Mathematics.

Part I Introduction.- Latin Squares Based on Groups.- When is a Latin Square Based on a Group?.- Part II Admissable Groups.- The Existence Problem for Complete Mappings: The Hall-Paige Conjecture.- Some Classes of Admissible Groups.- The Groups GL(n,q), SL(n,q), PGL(n,q), and PSL(n,q).- Minimal Counterexamples to the Hall-Paige Conjecture.- A Proof of the Hall-Paige Conjecture.- Part III Orthomorphism Graphs of Groups.- Orthomorphism Graphs of Groups.- Elementary Abelian Groups I.- Elementary Abelian Groups II.- Extensions of Orthomorphism Graphs.- ω(G) for Some Classes of Nonabelian Groups.- Groups of Small Order.- Part IV Additional Topics.- Projective Planes from Complete Sets of Orthomorphisms.- Related Topics.- Problems.- References.- Index.