Orthogonal Latin Squares Based on Groups

• Main Author: Evans, Anthony B. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Developments in Mathematics, 57
• Subjects: Combinatorics.; Group theory.; Group Theory and Generalizations.

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 construct...

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.