Nato Science Series C:

Generators and Relations in Groups and Geometries

Editors: Barlotti, A., Ellers, E.W., Plaumann, P., Strambach, K. (Eds.)

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About this book

Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated direction exist. The clue is to ask the right question. Classical geometry is a typical example in which the factorization of a motion into reflections or, more generally, of a collineation into central collineations, supplies valuable information on the geometric and algebraic structure. This mode of investigation has gained momentum since the end of last century. The tradition of geometric-algebraic interplay brought forward two branches of research which are documented in Parts I and II of these Proceedings. Part II deals with the theory of reflection geometry which culminated in Bachmann's work where the geometric information is encoded in properties of the group of motions expressed by relations in the generating involutions. This approach is the backbone of the classification of motion groups for the classical unitary and orthogonal planes. The axioms in this char­ acterization are natural and plausible. They provoke the study of consequences of subsets of axioms which also yield natural geometries whose exploration is rewarding. Bachmann's central axiom is the three reflection theorem, showing that the number of reflections needed to express a motion is of great importance.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $149.00
price for USA in USD
  • ISBN 978-94-011-3382-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $299.99
price for USA in USD
Softcover $199.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Generators and Relations in Groups and Geometries
Editors
  • A. Barlotti
  • E.W. Ellers
  • P. Plaumann
  • K. Strambach
Series Title
Nato Science Series C:
Series Volume
333
Copyright
1991
Publisher
Springer Netherlands
Copyright Holder
Kluwer Academic Publishers
eBook ISBN
978-94-011-3382-1
DOI
10.1007/978-94-011-3382-1
Hardcover ISBN
978-0-7923-1161-4
Softcover ISBN
978-94-010-5496-6
Series ISSN
1389-2185
Edition Number
1
Number of Pages
XV, 447
Topics