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Orthogonal Latin Squares Based on Groups

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Orthogonal Latin Squares Based on Groups/ by Anthony B. Evans.
作者:	Evans, Anthony B.
面頁冊數:	XV, 537 p. 90 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Combinatorics. -
電子資源:	https://doi.org/10.1007/978-3-319-94430-2
ISBN:	9783319944302

Orthogonal Latin Squares Based on Groups
Evans, Anthony B.

Orthogonal Latin Squares Based on Groups[electronic resource] /by Anthony B. Evans. - 1st ed. 2018. - XV, 537 p. 90 illus.online resource. - Developments in Mathematics,571389-2177 ;. - Developments in Mathematics,41.

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.

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. .

ISBN: 9783319944302

Standard No.: 10.1007/978-3-319-94430-2doiSubjects--Topical Terms:

669353
Combinatorics.

LC Class. No.: QA164-167.2

Dewey Class. No.: 511.6

Orthogonal Latin Squares Based on Groups
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505 0 $a 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.
520 $a 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. .
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