Theory of K-Loops

  • Authors
  • Hubert┬áKiechle

Part of the Lecture Notes in Mathematics book series (LNM, volume 1778)

Table of contents

  1. Front Matter
    Pages I-X
  2. Hubert Kiechle
    Pages 1-5
  3. Hubert Kiechle
    Pages 7-22
  4. Hubert Kiechle
    Pages 23-42
  5. Hubert Kiechle
    Pages 53-58
  6. Hubert Kiechle
    Pages 59-64
  7. Hubert Kiechle
    Pages 65-81
  8. Hubert Kiechle
    Pages 83-102
  9. Hubert Kiechle
    Pages 103-106
  10. Hubert Kiechle
    Pages 137-142
  11. Hubert Kiechle
    Pages 151-164
  12. Hubert Kiechle
    Pages 165-170
  13. Hubert Kiechle
    Pages 171-180
  14. Hubert Kiechle
    Pages 181-186
  15. Back Matter
    Pages 190-194

About this book

Introduction

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.

Keywords

Bol loops Frobenius groups with many Involutions K-loop Kikkawa loops Vector space

Bibliographic information

  • DOI https://doi.org/10.1007/b83276
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43262-3
  • Online ISBN 978-3-540-45817-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book