1.

Record Nr.

UNISA996466662103316

Autore

Kiechle Hubert

Titolo

Theory of K-Loops [[electronic resource] /] / by Hubert Kiechle

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002

ISBN

3-540-45817-4

Edizione

[1st ed. 2002.]

Descrizione fisica

1 online resource (X, 186 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1778

Disciplina

512.2

Soggetti

Group theory

Group Theory and Generalizations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references (pages [171]-180) and index.

Nota di contenuto

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.

Sommario/riassunto

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.