03055nam 22005895 450 99646666210331620200705173438.03-540-45817-410.1007/b83276(CKB)1000000000233245(SSID)ssj0000327218(PQKBManifestationID)11232914(PQKBTitleCode)TC0000327218(PQKBWorkID)10297929(PQKB)10067211(DE-He213)978-3-540-45817-3(MiAaPQ)EBC6285617(MiAaPQ)EBC5578951(Au-PeEL)EBL5578951(OCoLC)1066196312(PPN)155219367(EXLCZ)99100000000023324520121227d2002 u| 0engurnn|008mamaatxtccrTheory of K-Loops[electronic resource] /by Hubert Kiechle1st ed. 2002.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (X, 186 p.) Lecture Notes in Mathematics,0075-8434 ;1778Bibliographic Level Mode of Issuance: Monograph3-540-43262-0 Includes bibliographical references (pages [171]-180) and index.Introduction -- Preliminaries -- Left Loops and Transversals -- The Left Inverse Property and Kikkawa Loops -- Isotopy Theory -- Nuclei and the Autotopism Group -- Bol Loops and K-Loops -- Frobenius Ggroups with Mmany Involutions -- Loops with Fibrations -- K-Loops from Classical Groups over Ordered Fields -- Relativistic Velocity Addition -- K-Loops from the General Linear Groups over Rings -- Derivations.The book contains the first systematic exposition of the current known theory of K-loops, as well as some new material. In particular, big classes of examples are constructed. The theory for sharply 2-transitive groups is generalized to the theory of Frobenius groups with many involutions. A detailed discussion of the relativistic velocity addition based on the author's construction of K-loops from classical groups is also included. The first chapters of the book can be used as a text, the later chapters are research notes, and only partially suitable for the classroom. The style is concise, but complete proofs are given. The prerequisites are a basic knowledge of algebra such as groups, fields, and vector spaces with forms.Lecture Notes in Mathematics,0075-8434 ;1778Group theoryGroup Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Group theory.Group Theory and Generalizations.512.2Kiechle Hubertauthttp://id.loc.gov/vocabulary/relators/aut66733MiAaPQMiAaPQMiAaPQBOOK996466662103316Theory of K-loops262259UNISA