03844nam 22004935 450 991030013020332120250609111809.03-319-94430-410.1007/978-3-319-94430-2(CKB)4100000005820456(DE-He213)978-3-319-94430-2(MiAaPQ)EBC5494733(PPN)229916589(MiAaPQ)EBC6236117(EXLCZ)99410000000582045620180817d2018 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierOrthogonal Latin Squares Based on Groups /by Anthony B. Evans1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XV, 537 p. 90 illus.)Developments in Mathematics,1389-2177 ;573-319-94429-0 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. .Developments in Mathematics,1389-2177 ;57Combinatorial analysisGroup theoryCombinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Group Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Combinatorial analysis.Group theory.Combinatorics.Group Theory and Generalizations.511.6Evans Anthony B.authttp://id.loc.gov/vocabulary/relators/aut60217BOOK9910300130203321Orthogonal Latin Squares Based on Groups1563709UNINA01766oam 2200481M 450 991108084800332120200213070530.2(CKB)46368949000041(DGPO)001197227(OCoLC)1065836211(EXLCZ)994636894900004120071213d1925 ua 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierBridge across St. Louis River between Superior, Wis., and Duluth, Minn. February 17, 1925. -- Ordered to be printedWashington, DC :[publisher not identified],1925.1 online resource (1 page)Senate report / 68th Congress, 2nd session. Senate ;no. 1142[United States congressional serial set] ;[serial set no. 8388]Batch processed record: Metadata reviewed, not verified. Some fields updated by batch processes.FDLP item number not assigned.Bridge construction industryBridgesDesign and constructionBridgesDuluth, MinnesotaSaint Louis River (Minnesota/Wisconsin)Superior, WisconsinLegislative materials.lcgftBridge construction industry.BridgesDesign and construction.Bridges.Ladd Edwin Fremont1859-1925Republican (ND)1902857WYUWYUOCLCOOCLCQBOOK9911080848003321Bridge across St. Louis River between Superior, Wis., and Duluth, Minn. February 17, 1925. -- Ordered to be printed4628115UNINA