000 02727nam a22004575i 4500
001 978-3-540-45817-3
003 DE-He213
005 20190213151328.0
007 cr nn 008mamaa
008 121227s2002 gw | s |||| 0|eng d
020 _a9783540458173
_9978-3-540-45817-3
024 7 _a10.1007/b83276
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBG
_2thema
082 0 4 _a512.2
_223
100 1 _aKiechle, Hubert.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aTheory of K-Loops
_h[electronic resource] /
_cby Hubert Kiechle.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2002.
300 _aX, 186 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1778
505 0 _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.
520 _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.
650 0 _aGroup theory.
650 1 4 _aGroup Theory and Generalizations.
_0http://scigraph.springernature.com/things/product-market-codes/M11078
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662184356
776 0 8 _iPrinted edition:
_z9783540432623
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1778
856 4 0 _uhttps://doi.org/10.1007/b83276
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10296
_d10296