Synopsis
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.
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Generators and Relations in Groups and Geometries (NATO Science Series C: Mathematical and Physical Sciences, Volume 333)
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(eds.) Generators and Relations in Groups and Geometries.
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Hardcover. Condition: Sehr gut. Dordrecht, Kluwer (1991). gr.8°. XV, 446 S. Hardbound. (slightly browned).- NATO ASI Series, Series C: Mathematical and Physical Sciences, Vol.333. Seller Inventory # 86691
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Generators and Relations in Groups and Geometries
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Condition: Sehr gut. Zustand: Sehr gut | Seiten: 468 | Sprache: Englisch | Produktart: Bücher | 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. Seller Inventory # 3019064/202
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Generators and Relations in Groups and Geometries
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ISBN 10: 0792311612
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Generators and Relations in Groups and Geometries (Nato Science Series C:, 333)
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Generators and Relations in Groups and Geometries
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Proceedings of the NATO Advanced Study Institute, Castelvecchio Pascoli, Lucca, Italy, April 1-14, 1990Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generat. Seller Inventory # 5966212
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Generators and Relations in Groups and Geometries
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Buch. Condition: Neu. Generators and Relations in Groups and Geometries | A. Barlotti (u. a.) | Buch | xv | Englisch | 1991 | Springer Netherland | EAN 9780792311614 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Seller Inventory # 101951055
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Generators and Relations in Groups and Geometries
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Buch. Condition: Neu. 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 GmbH, Tiergartenstr. 17, 69121 Heidelberg 468 pp. Englisch. Seller Inventory # 9780792311614
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Generators and Relations in Groups and Geometries
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Generators and Relations in Groups and Geometries
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9780792311614