A. I. Kostrikin

Around Burnside (eBook, PDF)

Übersetzer: Wiegold, James

• Format: PDF

Produktbeschreibung

This revised and updated English edition offers a highly competent presentation from a leading expert in the field of algebra. The translator is well known for important reseach results in this field.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 222
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642743245
• Artikelnr.: 53085408

Inhaltsangabe

1 Introduction.- 1. Historical Survey.- 2. Engel Lie Algebras: Definitions and Examples.- 3. The Locally Nilpotent Radical.- 4. Basic Conventions. Elementary Combinatorics.- 5. The Method of Sandwiches.- 6. Filtrations in Lie Algebras.- 7. Main results and Structure of Proofs.- 8. Commentary.- 2 The Descent to Sandwiches.- 1. Descent to nil-elements of index 3.- 2. Descent to Thin Sandwiches (General Case).- 3. Descent to Thin Sandwiches (the Case p > n).- 4. Descent from C2* to C(p-3)/2* 41.- 5. Commentary.- 3 Local Analysis on Thin Sandwiches.- 1. A First Footbridge Between Thin and Thick Sandwiches.- 2. A Second Footbridge Between Thin and Thick Sandwiches.- 3. Two Necessary Lemmas.- 4. Sandwich Algebras.- 5. Commentary.- 4 Proof of the Main Theorem.- 1. Pairs of Thin Sandwiches.- 2. Thick Pairs of Thin Sandwiches.- 3. Completion of the Proof of the Main Theorem.- 4. Commentary.- 5 Evolution of the Method of Sandwiches.- 1. Rehabilitation of False Sandwiches.- 2. A Geodesic Connecting Theorems 3.4.1 and 1.7.4.- 3. The Local Nilpotency of Sandwich Algebras.- 4. The Sandwich Radical and its Applications.- 5. Commentary.- 6 The Problem of Global Nilpotency.- 1. The Nilpotency Class of a Lie Algebra with En.- 2. Combination of Solubility and the Engel Condition En.- 3. Insolubility for n Close to p.- 4. Global Nilpotency for p > n.- 5. Commentary.- 7 Finite p-Groups and Lie Algebras.- 1. Fundamental Relations Between Groups and Lie Algebras.- 2. The Ideal of Relations (a general Survey).- 3. Multilinear Relations: Proofs of Theorems 2.3 and 2.4.- 4. Commentary.- Appendix I An Effective Version of the Proof of Theorem 1.7.4 in Terms of Recursive Functions (due toE. I. Zel'manov).- Appendix II A Short Biography of William Burnside (after A.R. Forsyth [52]).- Epilogue.- Notes Added in Proof.- References.- Author Index.- Notation.