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On fusion systems of component type /
This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof of the theorem classifying the...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
AMS, American Mathematical Society,
2019.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1236. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof of the theorem classifying the finite simple groups.Why should such a simplification be possible? Part of the answer lies in the fact that there are advantages to be gained by working with fusion systems rather than groups. In particular one can hope to avoid a proof of the B-Conjecture, a important but difficult result in finite group theory, established only with great effort.But in addition, the program involves a reorganization of the treatment of âĂIJgroups of component typeâĂİ, or perhaps more accurately, of âĂIJfusion systems of component typeâĂİ. The groups of component type should be viewed as âĂIJoddâĂİ groups, in that most examples are groups of Lie type over fields of odd order. The remaining simple groups should be viewed as âĂIJevenâĂİ groups, since most of the examples in this class are of Lie type over fields of even order. There are corresponding notions of âĂIJoddâĂİ and âĂIJevenâĂİ 2-fusion systems.In our program the class of odd groups, and/or fusion systems, is contracted in a carefully chosen manner, so as to avoid difficulties associated to certain âĂIJstandard form problemsâĂİ. This has the effect of greatly simplifying the treatment of the odd 2-fusion systems, and then also the treatment of the odd simple groups. Of course the flip side of such a reorganization is to enlarge the class of even objects, so that the approach may make it more difficult to treat that class. But it is our sense that the trade off should lead to a net simplification. This change in the partition of simple groups into odd and even groups is not dissimilar to the one in the program of Gorenstein, Lyons, and Solomon (hereafter referred to as GLS) to rewrite the proof of the classification. In the introduction, we expand upon these themes, making them a bit more precise, supplying some background, and eventually stating some of our major theorems. Then in the body of the paper, we fill in details and begin the actual program. |
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| Notas: | "January 2019, volume 257, number 1236 (sixth of 6 numbers)." |
| Descripción Física: | 1 online resource (v, 182 pages) |
| Bibliografía: | Includes bibliographical references (pages 181-182). |
| ISBN: | 9781470449551 1470449552 |
| ISSN: | 0065-9266 ; |