Theory of K-Loops / by Hubert Kiechle.

Format:

Book

Author/Creator:

Kiechle, Hubert, 1960- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1778.

Lecture Notes in Mathematics, 0075-8434 ; 1778

Language:

English

Subjects (All):

Group theory.

Group Theory and Generalizations.

Local Subjects:

Group Theory and Generalizations.

Physical Description:

1 online resource (X, 186 pages).

Contained In:

Springer eBooks

Place of Publication:

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

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783540458173

Access Restriction:

Restricted for use by site license.