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.
Author(s): Hubert Kiechle (auth.)
Series: Lecture Notes in Mathematics 1778
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2002
Language: English
Pages: 186
City: Berlin; New York
Tags: Group Theory and Generalizations
Introduction....Pages 1-5
1. Preliminaries....Pages 7-22
2. Left Loops and Transversals....Pages 23-42
3. The Left Inverse Property and Kikkawa Loops....Pages 43-52
4. Isotopy Theory....Pages 53-58
5. Nuclei and the Autotopism Group....Pages 59-64
6. Bol Loops and K-Loops....Pages 65-81
7. Frobenius Groups with Many Involutions....Pages 83-102
8. Loops with Fibrations....Pages 103-106
9. K-Loops from Classical Groups over Ordered Fields....Pages 107-136
10. Relativistic Velocity Addition....Pages 137-142
11. K-loops from the General Linear Groups over Rings....Pages 143-150
12. Derivations....Pages 151-164
Appendix....Pages 165-170
References....Pages 171-180
Index....Pages 181-186
