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| Author | : Chris Parker |
| Publisher | : American Mathematical Society |
| Total Pages | : 194 |
| Release | : 2024-01-26 |
| Genre | : Mathematics |
| ISBN | : 1470467291 |
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| Author | : Daniel Gorenstein |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 545 |
| Release | : 1994 |
| Genre | : Computers |
| ISBN | : 0821827774 |
The classification of finite simple groups is a landmark result of modern mathematics. This work presents critical aspects of the classification. It provides the classification of finite simple groups of special odd type (Theorems $\mathcal{C}_2$ and $\mathcal{C}_3$). It is suitable for graduate students and researchers interested in group theory.
| Author | : Michael Aschbacher |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821853368 |
Provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the 'even case', where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of 'noncharacteristic 2 type'.
| Author | : Chat Yin Ho |
| Publisher | : Walter de Gruyter |
| Total Pages | : 434 |
| Release | : 2008-08-22 |
| Genre | : Mathematics |
| ISBN | : 3110198126 |
This is a volume of research articles related to finite groups. Topics covered include the classification of finite simple groups, the theory of p-groups, cohomology of groups, representation theory and the theory of buildings and geometries. As well as more than twenty original papers on the latest developments, which will be of great interest to specialists, the volume contains several expository articles, from which students and non-experts can learn about the present state of knowledge and promising directions for further research. The Finite Groups 2003 conference was held in honor of John Thompson. The profound influence of his fundamental contributions is clearly visible in this collection of papers dedicated to him.
| Author | : James E. Humphreys |
| Publisher | : Cambridge University Press |
| Total Pages | : 248 |
| Release | : 2005-12-22 |
| Genre | : Mathematics |
| ISBN | : 9780521674546 |
Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne-Lusztig characters. One goal has been to make the subject more accessible to those working in neighboring parts of group theory, number theory, and topology.
| Author | : B. Hartley |
| Publisher | : Springer |
| Total Pages | : 480 |
| Release | : 1995-08-31 |
| Genre | : Mathematics |
| ISBN | : |
Proceedings of the NATO Advanced Study Institute, Istanbul, Turkey, 14--27 August 1994
| Author | : Inna Capdeboscq |
| Publisher | : American Mathematical Society |
| Total Pages | : 587 |
| Release | : 2023-10-23 |
| Genre | : Mathematics |
| ISBN | : 1470475537 |
This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see SURV/40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.
| Author | : Gerhard Michler |
| Publisher | : Cambridge University Press |
| Total Pages | : 638 |
| Release | : 2006-09-21 |
| Genre | : Mathematics |
| ISBN | : 0521866251 |
The first representation theoretic and algorithmic approach to the theory of abstract finite simple groups.
| Author | : Bertram A. F. Wehrfritz |
| Publisher | : World Scientific |
| Total Pages | : 138 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9789810238742 |
The theory of groups, especially of finite groups, is one of the most delightful areas of mathematics. Its proofs often have elegance and crystalline beauty. This textbook is intended for the reader who has been exposed to about three years of serious mathematics. The notion of a group appears widely in mathematics and even further afield in physics and chemistry, and the fundamental idea should be known to all mathematicians. In this textbook a purely algebraic approach is taken and the choice of material is based upon the notion of conjugacy. The aim is not only to cover basic material, but also to present group theory as a living, vibrant and growing discipline, by including references and discussion of some work up to the present day.
| Author | : Daniel Gorenstein |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 743 |
| Release | : 1983 |
| Genre | : Mathematics |
| ISBN | : 0821822764 |
Studies the generic finite simple group of characteristic 2 type whose proper subgroups are of known type. The authors' principal result (the Trichotomy Theorem) asserts that such a group has one of three precisely determined internal structures.
