LEADER 03055nam 22005895 450 001 996466662103316 005 20200705173438.0 010 $a3-540-45817-4 024 7 $a10.1007/b83276 035 $a(CKB)1000000000233245 035 $a(SSID)ssj0000327218 035 $a(PQKBManifestationID)11232914 035 $a(PQKBTitleCode)TC0000327218 035 $a(PQKBWorkID)10297929 035 $a(PQKB)10067211 035 $a(DE-He213)978-3-540-45817-3 035 $a(MiAaPQ)EBC6285617 035 $a(MiAaPQ)EBC5578951 035 $a(Au-PeEL)EBL5578951 035 $a(OCoLC)1066196312 035 $a(PPN)155219367 035 $a(EXLCZ)991000000000233245 100 $a20121227d2002 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aTheory of K-Loops$b[electronic resource] /$fby Hubert Kiechle 205 $a1st ed. 2002. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002. 215 $a1 online resource (X, 186 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1778 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-43262-0 320 $aIncludes bibliographical references (pages [171]-180) and index. 327 $aIntroduction -- 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. 330 $aThe book contains the first systematic exposition of the current known theory of K-loops, as well as some new material. In particular, big classes of examples are constructed. The theory for sharply 2-transitive groups is generalized to the theory of Frobenius groups with many involutions. A detailed discussion of the relativistic velocity addition based on the author's construction of K-loops from classical groups is also included. The first chapters of the book can be used as a text, the later chapters are research notes, and only partially suitable for the classroom. The style is concise, but complete proofs are given. The prerequisites are a basic knowledge of algebra such as groups, fields, and vector spaces with forms. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1778 606 $aGroup theory 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 615 0$aGroup theory. 615 14$aGroup Theory and Generalizations. 676 $a512.2 700 $aKiechle$b Hubert$4aut$4http://id.loc.gov/vocabulary/relators/aut$066733 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466662103316 996 $aTheory of K-loops$9262259 997 $aUNISA