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Lecture Notes in Mathematics

Theory of K-Loops

Authors: Kiechle, Hubert

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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)


Table of contents (16 chapters)

Table of contents (16 chapters)

Buy this book

eBook $34.99
price for USA in USD
  • ISBN 978-3-540-45817-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA in USD
  • ISBN 978-3-540-43262-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Theory of K-Loops
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1778
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-45817-3
DOI
10.1007/b83276
Softcover ISBN
978-3-540-43262-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 186
Topics

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