Around Burnside

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.