The Resource Orthogonal Latin Squares Based on Groups, by Anthony B. Evans, (electronic resource)
Orthogonal Latin Squares Based on Groups, by Anthony B. Evans, (electronic resource)
Resource Information
The item Orthogonal Latin Squares Based on Groups, by Anthony B. Evans, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Orthogonal Latin Squares Based on Groups, by Anthony B. Evans, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 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.
 Language
 eng
 Extent
 1 online resource (XV, 537 pages)
 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 HallPaige 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 HallPaige Conjecture
 A Proof of the HallPaige 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
 Isbn
 9783319944302
 Label
 Orthogonal Latin Squares Based on Groups
 Title
 Orthogonal Latin Squares Based on Groups
 Statement of responsibility
 by Anthony B. Evans
 Language
 eng
 Summary
 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.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Evans, Anthony B
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement

 Springer eBooks.
 Springer eBooks
 Developments in Mathematics,
 Series volume
 57
 http://library.link/vocab/subjectName

 Combinatorics
 Group theory
 Mathematics
 Label
 Orthogonal Latin Squares Based on Groups, by Anthony B. Evans, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 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 HallPaige 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 HallPaige Conjecture  A Proof of the HallPaige 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
 Control code
 9783319944302
 Dimensions
 unknown
 Extent
 1 online resource (XV, 537 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319944302
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 90 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1048932113
 Label
 Orthogonal Latin Squares Based on Groups, by Anthony B. Evans, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 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 HallPaige 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 HallPaige Conjecture  A Proof of the HallPaige 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
 Control code
 9783319944302
 Dimensions
 unknown
 Extent
 1 online resource (XV, 537 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319944302
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 90 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1048932113
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/OrthogonalLatinSquaresBasedonGroupsby/gRH2_wMJT0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/OrthogonalLatinSquaresBasedonGroupsby/gRH2_wMJT0/">Orthogonal Latin Squares Based on Groups, by Anthony B. Evans, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>