Generators and Relations in Groups and Geometries:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1991
|
| Schriftenreihe: | NATO ASI Series
333 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XV, 447 p) |
| ISBN: | 9789401133821 9789401054966 |
| ISSN: | 1389-2185 |
| DOI: | 10.1007/978-94-011-3382-1 |
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| 246 | 1 | 3 | |a Proceedings of the NATO Advanced Study Institute, Castelvecchio Pascoli, Lucca, Italy, April 1-14, 1990 |
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| 500 | |a 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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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-94-011-3382-1 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:20:58Z |
| institution | BVB |
| isbn | 9789401133821 9789401054966 |
| issn | 1389-2185 |
| language | English |
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| spelling | Barlotti, A. Verfasser aut Generators and Relations in Groups and Geometries edited by A. Barlotti, E. W. Ellers, P. Plaumann, K. Strambach Proceedings of the NATO Advanced Study Institute, Castelvecchio Pascoli, Lucca, Italy, April 1-14, 1990 Dordrecht Springer Netherlands 1991 1 Online-Ressource (XV, 447 p) txt rdacontent c rdamedia cr rdacarrier NATO ASI Series 333 1389-2185 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 Mathematics Field theory (Physics) Group theory Matrix theory Global differential geometry Group Theory and Generalizations Field Theory and Polynomials Linear and Multilinear Algebras, Matrix Theory Differential Geometry Mathematik Ellers, E. W. Sonstige oth Plaumann, P. Sonstige oth Strambach, K. Sonstige oth https://doi.org/10.1007/978-94-011-3382-1 Verlag Volltext |
| spellingShingle | Barlotti, A. Generators and Relations in Groups and Geometries Mathematics Field theory (Physics) Group theory Matrix theory Global differential geometry Group Theory and Generalizations Field Theory and Polynomials Linear and Multilinear Algebras, Matrix Theory Differential Geometry Mathematik |
| title | Generators and Relations in Groups and Geometries |
| title_alt | Proceedings of the NATO Advanced Study Institute, Castelvecchio Pascoli, Lucca, Italy, April 1-14, 1990 |
| title_auth | Generators and Relations in Groups and Geometries |
| title_exact_search | Generators and Relations in Groups and Geometries |
| title_full | Generators and Relations in Groups and Geometries edited by A. Barlotti, E. W. Ellers, P. Plaumann, K. Strambach |
| title_fullStr | Generators and Relations in Groups and Geometries edited by A. Barlotti, E. W. Ellers, P. Plaumann, K. Strambach |
| title_full_unstemmed | Generators and Relations in Groups and Geometries edited by A. Barlotti, E. W. Ellers, P. Plaumann, K. Strambach |
| title_short | Generators and Relations in Groups and Geometries |
| title_sort | generators and relations in groups and geometries |
| topic | Mathematics Field theory (Physics) Group theory Matrix theory Global differential geometry Group Theory and Generalizations Field Theory and Polynomials Linear and Multilinear Algebras, Matrix Theory Differential Geometry Mathematik |
| topic_facet | Mathematics Field theory (Physics) Group theory Matrix theory Global differential geometry Group Theory and Generalizations Field Theory and Polynomials Linear and Multilinear Algebras, Matrix Theory Differential Geometry Mathematik |
| url | https://doi.org/10.1007/978-94-011-3382-1 |
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