Generators and Relations in Groups and Geometries

Language: English

Published by Springer, Springer Netherlands Sep 2012, 2012

9401054967 / 9789401054966

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 468 pp. Englisch.…

Seller Inventory # 9789401054966

Title
Generators and Relations in Groups and Geometries
Author
A. Barlotti
Publisher
Springer, Springer Netherlands Sep 2012
Publication year
2012
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
9401054967
ISBN 13
9789401054966
Item weight
703 grams
Dimensions
235x155x26 mm

buchversandmimpf2000

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