Symmetric generation of groups: with applications to many of the sporadic finite simple groups
Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups. But gaining familiarity with these groups presents problems for two reasons. Firstly, they were discovered in many different ways, so to understand their constructions in depth one needs to...
Gespeichert in:
| Beteilige Person: | |
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
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| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 111 |
| Links: | https://doi.org/10.1017/CBO9780511661792 |
| Zusammenfassung: | Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups. But gaining familiarity with these groups presents problems for two reasons. Firstly, they were discovered in many different ways, so to understand their constructions in depth one needs to study lots of different techniques. Secondly, since each of them is in a sense recording some exceptional symmetry in spaces of certain dimensions, they are by their nature highly complicated objects with a rich underlying combinatorial structure. Motivated by initial results which showed that the Mathieu groups can be generated by highly symmetrical sets of elements, which themselves have a natural geometric definition, the author develops from scratch the notion of symmetric generation. He exploits this technique by using it to define and construct many of the sporadic simple groups including all the Janko groups and the Higman-Sims group. For researchers and postgraduates. |
| Umfang: | 1 Online-Ressource (xiv, 317 Seiten) |
| ISBN: | 9780511661792 |
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| spelling | Curtis, Robert 1946- Symmetric generation of groups with applications to many of the sporadic finite simple groups Robert T. Curtis Cambridge Cambridge University Press 2007 1 Online-Ressource (xiv, 317 Seiten) txt c cr Encyclopedia of mathematics and its applications volume 111 Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups. But gaining familiarity with these groups presents problems for two reasons. Firstly, they were discovered in many different ways, so to understand their constructions in depth one needs to study lots of different techniques. Secondly, since each of them is in a sense recording some exceptional symmetry in spaces of certain dimensions, they are by their nature highly complicated objects with a rich underlying combinatorial structure. Motivated by initial results which showed that the Mathieu groups can be generated by highly symmetrical sets of elements, which themselves have a natural geometric definition, the author develops from scratch the notion of symmetric generation. He exploits this technique by using it to define and construct many of the sporadic simple groups including all the Janko groups and the Higman-Sims group. For researchers and postgraduates. Erscheint auch als Druck-Ausgabe 9780521857215 |
| spellingShingle | Curtis, Robert 1946- Symmetric generation of groups with applications to many of the sporadic finite simple groups |
| title | Symmetric generation of groups with applications to many of the sporadic finite simple groups |
| title_auth | Symmetric generation of groups with applications to many of the sporadic finite simple groups |
| title_exact_search | Symmetric generation of groups with applications to many of the sporadic finite simple groups |
| title_full | Symmetric generation of groups with applications to many of the sporadic finite simple groups Robert T. Curtis |
| title_fullStr | Symmetric generation of groups with applications to many of the sporadic finite simple groups Robert T. Curtis |
| title_full_unstemmed | Symmetric generation of groups with applications to many of the sporadic finite simple groups Robert T. Curtis |
| title_short | Symmetric generation of groups |
| title_sort | symmetric generation of groups with applications to many of the sporadic finite simple groups |
| title_sub | with applications to many of the sporadic finite simple groups |
| work_keys_str_mv | AT curtisrobert symmetricgenerationofgroupswithapplicationstomanyofthesporadicfinitesimplegroups |