» » The Classification of Finite Simple Groups: Volume 1: Groups of Noncharacteristic 2 Type (University Series in Mathematics)

Fb2 The Classification of Finite Simple Groups: Volume 1: Groups of Noncharacteristic 2 Type (University Series in Mathematics) ePub

by Daniel Gorenstein

Category: Mathematics
Subcategory: Science books
Author: Daniel Gorenstein
ISBN: 0306413051
ISBN13: 978-0306413056
Language: English
Publisher: Springer; 1983 edition (September 30, 1983)
Pages: 487
Fb2 eBook: 1417 kb
ePub eBook: 1278 kb
Digital formats: azw lit mobi docx

Outline of the classification of groups of characteristic 2 type Then in Volume 1 he described the treatment of xi. xii. PREFACE. the groups of odd characteristic in detail.

Outline of the classification of groups of characteristic 2 type. 83. Chapter 3. e(G) ≤ 2: The classification of quasithin groups . Introduction: The Thompson Strategy . Preface The present book, The Classification of Finite Simple Groups: Groups of Characteristic 2 Type, completes a project of giving an outline of the proof of the Classification of the Finite Simple Groups (CFSG). The project was begun by Daniel Gorenstein in 1983 with his book -which he subtitled Volume 1: Groups of Noncharacteristic 2 Type. Then in Volume 1 he described the treatment of xi.

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. However, this book provides much more. Chapter 0 is a modern overview of the logical structure of the entire classification. Chapter 1 is a concise but complete outline of the odd case with updated references, while Chapter 2 sets the stage for the remainder of the book with a similar outline of the even case.

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four broad classes described below

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four broad classes described below. These groups can be seen as the basic building blocks of all finite groups, in a way reminiscent of the way the prime numbers are the basic building blocks of the natural numbers. The Jordan–Hölder theorem is a more precise way of stating this fact about finite groups

But the classification of all finite simple groups is such a theorem-its complete proof, developed over a 30-year period by about 100 group theorists, is the union of some 500 journal articles covering approximately 10,000 printed pages.

But the classification of all finite simple groups is such a theorem-its complete proof, developed over a 30-year period by about 100 group theorists, is the union of some 500 journal articles covering approximately 10,000 printed pages

The Classification Theorem is one of the main achievements of 20th century mathematics, but its .

The Classification Theorem is one of the main achievements of 20th century mathematics, but its proof has not yet been completely extricated from the journal literature in which it first appeared. This is the second volume in a series devoted to the presentation of a reorganized and simplified proof of the classification of the finite simple groups. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series.

Series: University Series in Mathematics. Paperback: 487 pages. ISBN-13: 978-1461336877. Product Dimensions: . x . inches. Back to top. Get to Know Us. Careers.

of finite simple groups is a landmark result of modern mathematics. First, Aschbacher characterized the finite simple groups of Lie type in odd characteristic.

The classification of finite simple groups is a landmark result of modern mathematics.

But the classification of all finite simple groups is such a theorem-its complete proof, developed over a 30-year period by about 100 group theorists, is the union of some 500 journal articles covering approximately 10,000 printed pages.

But the classification of all finite simple groups is such a theorem-its complete proof, developed over a 30-year period by about 100 group theorists, is the union of some 500 journal articles covering approximately 10,000 printed pages

The classication of the nite simple groups, Daniel Gorenstein, Richard . Groups of generic type D. The Classication Grid: The Stages of the Proof 17.

The classication of the nite simple groups, Daniel Gorenstein, Richard Lyons, Ronald Solomon. p. cm. (Mathematical surveys and monographs, v. 40, number 1) Includes bibliographical references and index. Introduction to the Series A. The Finite Simple Groups 1. Simple groups 2. K-groups B. The Structure of Finite Groups 3. The Jordan-H older theorem and simple groups 4. The generalized Fitting subgroup and quasisimple groups 5. p -cores and p-components 6. The embedding of p -cores and p-components 7. Terminal and p-terminal p-components 8. p-constrained.

This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with.

This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes.

Never before in the history of mathematics has there been an individual theorem whose proof has required 10,000 journal pages of closely reasoned argument. Who could read such a proof, let alone communicate it to others? But the classification of all finite simple groups is such a theorem-its complete proof, developed over a 30-year period by about 100 group theorists, is the union of some 500 journal articles covering approximately 10,000 printed pages. How then is one who has lived through it all to convey the richness and variety of this monumental achievement? Yet such an attempt must be made, for without the existence of a coherent exposition of the total proof, there is a very real danger that it will gradually become lost to the living world of mathematics, buried within the dusty pages of forgotten journals. For it is almost impossible for the uninitiated to find the way through the tangled proof without an experienced guide; even the 500 papers themselves require careful selection from among some 2,000 articles on simple group theory, which together include often attractive byways, but which serve only to delay the journey.
Related to The Classification of Finite Simple Groups: Volume 1: Groups of Noncharacteristic 2 Type (University Series in Mathematics)
Applied Proof Theory: Proof Interpretations and their Use in Mathematics (Springer Monographs in Mathematics) eBook
Fb2 Applied Proof Theory: Proof Interpretations and their Use in Mathematics (Springer Monographs in Mathematics) ePub
The Four-Color Theorem: History, Topological Foundations, and Idea of Proof eBook
Fb2 The Four-Color Theorem: History, Topological Foundations, and Idea of Proof ePub
Invitation to the Mathematics of Fermat-Wiles eBook
Fb2 Invitation to the Mathematics of Fermat-Wiles ePub
The Structure of Affine Buildings. (AM-168) (Annals of Mathematics Studies) eBook
Fb2 The Structure of Affine Buildings. (AM-168) (Annals of Mathematics Studies) ePub
Groups: An Introduction to Ideas and Methods of the Theory of Groups (UNITEXT) eBook
Fb2 Groups: An Introduction to Ideas and Methods of the Theory of Groups (UNITEXT) ePub
Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 (Annals of Mathematics Studies) eBook
Fb2 Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 (Annals of Mathematics Studies) ePub
The Classification of the Finite Simple Groups, Number 4 (Mathematical Surveys Monographs) (No.4) eBook
Fb2 The Classification of the Finite Simple Groups, Number 4 (Mathematical Surveys  Monographs) (No.4) ePub
Fermat's Last Theorem: New Simple Proof eBook
Fb2 Fermat's Last Theorem: New Simple Proof ePub
The Arcata Conference on Representations of Finite Groups (Proceedings of Symposia in Pure Mathematics) eBook
Fb2 The Arcata Conference on Representations of Finite Groups (Proceedings of Symposia in Pure Mathematics) ePub