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Theory of K-Loops

  • Book
  • © 2002

Overview

Authors:
  1. Hubert Kiechle
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1778)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Hubert Kiechle
    Pages 1-5

  3. 1. Preliminaries

    • Hubert Kiechle
    Pages 7-22

  4. 2. Left Loops and Transversals

    • Hubert Kiechle
    Pages 23-42

  5. 3. The Left Inverse Property and Kikkawa Loops

    • Hubert Kiechle
    Pages 43-52

  6. 4. Isotopy Theory

    • Hubert Kiechle
    Pages 53-58

  7. 5. Nuclei and the Autotopism Group

    • Hubert Kiechle
    Pages 59-64

  8. 6. Bol Loops and K-Loops

    • Hubert Kiechle
    Pages 65-81

  9. 7. Frobenius Groups with Many Involutions

    • Hubert Kiechle
    Pages 83-102

  10. 8. Loops with Fibrations

    • Hubert Kiechle
    Pages 103-106

  11. 9. K-Loops from Classical Groups over Ordered Fields

    • Hubert Kiechle
    Pages 107-136

  12. 10. Relativistic Velocity Addition

    • Hubert Kiechle
    Pages 137-142

  13. 11. K-loops from the General Linear Groups over Rings

    • Hubert Kiechle
    Pages 143-150

  14. 12. Derivations

    • Hubert Kiechle
    Pages 151-164

  15. Appendix

    • Hubert Kiechle
    Pages 165-170

  16. References

    • Hubert Kiechle
    Pages 171-180

  17. Index

    • Hubert Kiechle
    Pages 181-186

  18. Back Matter

    Pages 190-194
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Keywords

About this book

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.

Reviews

From the reviews:

"The approach of this book is based on the foundations of geometry and on group theory … . The book is self-contained … . This well written book can serve as a reference and a source of constructions for researchers of the theory of non-associative structures. Also, thanks to the didactic presentation, I can also recommend it for motivated graduate students and university teachers." (Gabor P. Nagy, Acta Scientiarum Mathematicarum, Vol. 71, 2005)

"This book, which is based on the author’s habilitation thesis, is about a class of loops which have been intensively studied in the last decade and a half or so. … This book is a guide and reference to K-loops, especially to the work of Karzel’s students and followers. It is also a good source for the relationship between K-loops and other varieties of loops. … The book is quite readable and is certainly something that everyone working on these loops will find quite useful." (Michael K. Kinyon, Mathematical Reviews, Issue 2003 d)

Bibliographic Information

  • Book Title: Theory of K-Loops

  • Authors: Hubert Kiechle

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b83276

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-43262-3Published: 25 March 2002

  • eBook ISBN: 978-3-540-45817-3Published: 12 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 186

  • Topics: Group Theory and Generalizations

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