Abstract Root Subgroups and Simple Groups of Lie-Type:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2001
|
| Schriftenreihe: | Monographs in Mathematics
95 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-0348-7594-3 |
| Beschreibung: | It was already in 1964 [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G. This question is quite natural, since the class of transpositions of a symmetric group possesses this property. Namely the order of the product (ij)(kl) is 1, 2 or 3 according as {i,j} n {k,l} consists of 2,0 or 1 element. In fact, if I{i,j} n {k,I}1 = 1 and j = k, then (ij)(kl) is the 3-cycle (ijl). After the preliminary papers [Fis66] and [Fis64] he succeeded in [Fis71J, [Fis69] to classify all finite "nearly" simple groups generated by such a class of 3-transpositions, thereby discovering three new finite simple groups called M(22), M(23) and M(24). But even more important than his classification theorem was the fact that he originated a new method in the study of finite groups, which is called "internal geometric analysis" by D. Gorenstein in his book: Finite Simple Groups, an Introduction to their Classification. In fact D. Gorenstein writes that this method can be regarded as second in importance for the classification of finite simple groups only to the local group-theoretic analysis created by J. Thompson |
| Umfang: | 1 Online-Ressource (XIII, 389 p) |
| ISBN: | 9783034875943 9783034875967 |
| DOI: | 10.1007/978-3-0348-7594-3 |
Internformat
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| 500 | |a It was already in 1964 [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G. This question is quite natural, since the class of transpositions of a symmetric group possesses this property. Namely the order of the product (ij)(kl) is 1, 2 or 3 according as {i,j} n {k,l} consists of 2,0 or 1 element. In fact, if I{i,j} n {k,I}1 = 1 and j = k, then (ij)(kl) is the 3-cycle (ijl). After the preliminary papers [Fis66] and [Fis64] he succeeded in [Fis71J, [Fis69] to classify all finite "nearly" simple groups generated by such a class of 3-transpositions, thereby discovering three new finite simple groups called M(22), M(23) and M(24). But even more important than his classification theorem was the fact that he originated a new method in the study of finite groups, which is called "internal geometric analysis" by D. Gorenstein in his book: Finite Simple Groups, an Introduction to their Classification. In fact D. Gorenstein writes that this method can be regarded as second in importance for the classification of finite simple groups only to the local group-theoretic analysis created by J. Thompson | ||
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Datensatz im Suchindex
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| doi_str_mv | 10.1007/978-3-0348-7594-3 |
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| id | DE-604.BV042421943 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:45Z |
| institution | BVB |
| isbn | 9783034875943 9783034875967 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857360 |
| oclc_num | 1185504663 |
| open_access_boolean | |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XIII, 389 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser Basel |
| record_format | marc |
| series2 | Monographs in Mathematics |
| spellingShingle | Timmesfeld, Franz Georg Abstract Root Subgroups and Simple Groups of Lie-Type Mathematics Group theory Group Theory and Generalizations Mathematik Lie-Gruppe (DE-588)4035695-4 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd Untergruppe (DE-588)4224972-7 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4295326-1 (DE-588)4224972-7 |
| title | Abstract Root Subgroups and Simple Groups of Lie-Type |
| title_auth | Abstract Root Subgroups and Simple Groups of Lie-Type |
| title_exact_search | Abstract Root Subgroups and Simple Groups of Lie-Type |
| title_full | Abstract Root Subgroups and Simple Groups of Lie-Type by Franz Georg Timmesfeld |
| title_fullStr | Abstract Root Subgroups and Simple Groups of Lie-Type by Franz Georg Timmesfeld |
| title_full_unstemmed | Abstract Root Subgroups and Simple Groups of Lie-Type by Franz Georg Timmesfeld |
| title_short | Abstract Root Subgroups and Simple Groups of Lie-Type |
| title_sort | abstract root subgroups and simple groups of lie type |
| topic | Mathematics Group theory Group Theory and Generalizations Mathematik Lie-Gruppe (DE-588)4035695-4 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd Untergruppe (DE-588)4224972-7 gnd |
| topic_facet | Mathematics Group theory Group Theory and Generalizations Mathematik Lie-Gruppe Lineare algebraische Gruppe Untergruppe |
| url | https://doi.org/10.1007/978-3-0348-7594-3 |
| work_keys_str_mv | AT timmesfeldfranzgeorg abstractrootsubgroupsandsimplegroupsoflietype |