The Classification of the Finite Simple Groups, Number 7
Part III, Chapters 7-11: the Generic Case, Stages 3b and 4a
Seiten
2018
American Mathematical Society (Verlag)
978-0-8218-4069-6 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-4069-6 (ISBN)
The classification of finite simple groups is a landmark result of modern mathematics. This volume is part of a series of monographs being published by the AMS that represent the culmination of a century-long project. Part seven of the series, this is the middle volume of a trilogy treating the Generic Case.
The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1-40.7 and future volumes) represents the culmination of a century-long project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4-40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13.
The book is suitable for graduate students and researchers interested in the theory of finite groups.
The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1-40.7 and future volumes) represents the culmination of a century-long project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4-40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13.
The book is suitable for graduate students and researchers interested in the theory of finite groups.
Daniel Gorenstein and Richard Lyons, Rutgers University, Piscataway, NY. Ronald Solomon, The Ohio State University, Columbus, OH.
The stages of theorem $/mathscr{C}^*_7$
General group-theoretic lemmas
Theorem $/mathscr{C}^*_7$: Stage 3b
Theorem $/mathscr{C}^*_7$, stage 4a: Constructing a large alternating subgroup $G_0$
Properties of $/mathscr{K}$-groups
Bibliography
Index
| Erscheinungsdatum | 07.01.2018 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 790 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8218-4069-X / 082184069X |
| ISBN-13 | 978-0-8218-4069-6 / 9780821840696 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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