The Classification of the Finite Simple Groups, Number 8
Part III, Chapters 12-17: the Generic Case, Completed
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-4189-0 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4189-0 (ISBN)
This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach the completion of the proof of Theorem O.
This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series--the completion of the proof of the following theorem: Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups.
Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series.
This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series--the completion of the proof of the following theorem: Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups.
Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series.
Daniel Gorenstein and Richard Lyons, Rutgers University, Piscataway, NJ. Ronald Solomon, The Ohio State University, Columbus, OH.
Introduction
Recognition theory
Theorem $/mathscr{C}^*_7$: Stage 4b$ $--A large Lie-type subgroup $G_0$ for $p=2$
Theorem $/mathscr{C}^*_7$: Stage 4b$ $--A large Lie-type subgroup $G_0$ for $p>2$
Theorem $/mathscr{C}^*_7$: Stage 5$ $: $G=G_0$
Preliminary properties of $/mathscr{K}$-groups
Bibliography
Index
| Erscheinungsdatum | 04.02.2019 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 1005 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-4189-6 / 1470441896 |
| ISBN-13 | 978-1-4704-4189-0 / 9781470441890 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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