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＜電子ブック＞
Theory of K-Loops / by Hubert Kiechle
(Lecture Notes in Mathematics. ISSN:16179692 ; 1778)

版	1st ed. 2002.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	X, 186 p : online resource
著者標目	*Kiechle, Hubert author SpringerLink (Online service)
件　名	LCSH:Group theory FREE:Group Theory and Generalizations
一般注記	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 HTTP:URL=https://doi.org/10.1007/b83276

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