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Titlebook: Orthogonal Latin Squares Based on Groups; Anthony B. Evans Book 2018 Springer International Publishing AG, part of Springer Nature 2018 Or

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書目名稱Orthogonal Latin Squares Based on Groups
編輯Anthony B. Evans
視頻videohttp://file.papertrans.cn/705/704704/704704.mp4
概述Presents the first unified proof of the Hall–Paige conjecture.Discusses the actions of groups on designs derived from latin squares.Includes an extensive list of open problems on the construction and
叢書名稱Developments in Mathematics
圖書封面Titlebook: Orthogonal Latin Squares Based on Groups;  Anthony B. Evans Book 2018 Springer International Publishing AG, part of Springer Nature 2018 Or
描述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 fi
出版日期Book 2018
關鍵詞Orthomorphism; Complete mapping; Latin square; MOLS; Difference matrix; Orthogonality; Finite group; Finite
版次1
doihttps://doi.org/10.1007/978-3-319-94430-2
isbn_softcover978-3-030-06850-9
isbn_ebook978-3-319-94430-2Series ISSN 1389-2177 Series E-ISSN 2197-795X
issn_series 1389-2177
copyrightSpringer International Publishing AG, part of Springer Nature 2018
The information of publication is updating

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Minimal Counterexamples to the Hall-Paige Conjecturethat any minimal counterexample must be “close” to being a simple group. In 1992 Evans tried to improve on this by extending complete mappings of ., a subgroup of . of index 2, to complete mappings of .; and complete mappings of .∕., ., to complete mappings of .. Evans’ proofs require that certain t
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A Proof of the Hall-Paige Conjecture finite simple group of Lie type, with the possible exception of.(2)., the Tits group, could be a minimal counterexample to this conjecture. As the alternating groups were proved to be admissible in 1955 by Hall and Paige, and the Mathieu groups were proved admissible in 1993 by Dalla Volta and Gavi
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Orthomorphism Graphs of Groupsphism graphs: graphs whose vertices are orthomorphisms, and in which adjacency implies orthogonality. In this chapter we introduce orthomorphism graphs of groups. We describe the main problems of interest in the study of orthomorphism graphs, and we describe automorphisms and congruences of orthomor
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