Applying the Classification of Finite Simple Groups : a User's Guide

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Mathematical Surveys and Monographs ; v. 230Publisher: Providence : American Mathematical Society, 2018Description: 1 Online-Ressource (248 pages)Subject(s): Additional physical formats: 1470442914 | 9781470442910 | 1470446820 | 9781470446826 | Erscheint auch als: Applying the classification of finite simple groups. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2018. xiii, 231 Seiten | Print version: Applying the Classification of Finite Simple Groups : A User's Guide. Providence : American Mathematical Society, ©2018DDC classification:
  • 512/.2
MSC: MSC: *20-02 | 20D05 | 20Bxx | 20Cxx | 20E32Online resources: Summary: 5.2. Representations for Lie-type groups5.3. Representations for sporadic groups; Applications to Alperin's conjecture; 5.4. Introduction: The Alperin Weight Conjecture (AWC); 5.5. Reductions of the AWC to simple groups; 5.6. A closer look at verification for the Lie-type case; A glimpse of some other applications of representations; Chapter 6. Maximal subgroups and primitive representations; Introduction: Maximal subgroups and primitive actions; 6.1. Maximal subgroups of symmetric and alternating groups; 6.2. Maximal subgroups of Lie-type groups; 6.3. Maximal subgroups of sporadic groupsSummary: Chapter 2. Outline of the proof of the CFSG: Some main ideas2.0. A start: Proving the Odd/Even Dichotomy Theorem; 2.1. Treating the Odd Case: Via standard form; 2.2. Treating the Even Case: Via trichotomy and standard type; 2.3. Afterword: Comparison with later CFSG approaches; Applying the CFSG toward Quillen's Conjecture on _{ }(); 2.4. Introduction: The poset _{ }() and the contractibility conjecture; 2.5. Quillen-dimension and the solvable case; 2.6. The reduction of the -solvable case to the solvable case; 2.7. Other uses of the CFSG in the Aschbacher-Smith proofSummary: Chapter 4. Recognition theorems for simple groupsIntroduction: Finishing classification problems; 4.1. Recognizing alternating groups; 4.2. Recognizing Lie-type groups; 4.3. Recognizing sporadic groups; Applications to recognizing some quasithin groups; 4.4. Background: 2-local structure in the quasithin analysis; 4.5. Recognizing rank-2 Lie-type groups; 4.6. Recognizing the Rudvalis group; Chapter 5. Representation theory of simple groups; Introduction: Some standard general facts about representations; 5.1. Representations for alternating and symmetric groupsSummary: Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the ""quasithin"" part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite GrouPPN: PPN: 1026359716Package identifier: Produktsigel: ZDB-4-NLEBK
No physical items for this record
KIT – The Research University in the Helmholtz Association                         Home | Impressum | Datenschutz | Barrierefreiheit | KIT