Overview

This monograph presents a unified exposition of latin squares and mutually orthogonal sets of latin squares based on groups. Its focus is on orthomorphisms and complete mappings of finite groups, while also offering a complete proof of the Hall–Paige conjecture. The use of latin squares in constructions of nets, affine planes, projective planes, and transversal designs also motivates this inquiry.   The text begins by introducing fundamental concepts, like the tests for determining whether a latin square is based on a group, as well as orthomorphisms and complete mappings. From there, it describes the existence problem for complete mappings of groups, building up to the proof of the Hall–Paige conjecture. The third part presents a comprehensive study of orthomorphism graphs of groups, while the last part provides a discussion of Cartesian projective planes, related combinatorial structures, and a list of open problems.   Expanding the author’s 1992 monograph, Orthomorphism Graphs of Groups, this book is an essential reference tool for mathematics researchers or graduate students tackling latin square problems in combinatorics. Its presentation draws on a basic understanding of finite group theory, finite field theory, linear algebra, and elementary number theory—more advanced theories are introduced in the text as needed. 

Full Product Details

Author:   Anthony B. Evans
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   1st ed. 2018
Volume:   57
Weight:   0.992kg
ISBN:  

9783319944296

ISBN 10:   3319944290
Pages:   537
Publication Date:   05 September 2018
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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.

Reviews

Author Information

​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.

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions