Coverart for item
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)

Label
Orthogonal Latin Squares Based on Groups
Title
Orthogonal Latin Squares Based on Groups
Statement of responsibility
by Anthony B. Evans
Creator
Subject
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.--
Member of
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)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-94430-2
Instantiates
Publication
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 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
Control code
978-3-319-94430-2
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, non-commercial 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)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-94430-2
Publication
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 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
Control code
978-3-319-94430-2
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, non-commercial 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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