Author | Kostrikin, A. I. author |
---|---|
Title | Around Burnside [electronic resource] / by A. I. Kostrikin |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1990 |
Connect to | http://dx.doi.org/10.1007/978-3-642-74324-5 |
Descript | XII, 222 p. online resource |
1 Introduction -- ยง 1. Historical Survey -- ยง 2. Engel Lie Algebras: Definitions and Examples -- ยง 3. The Locally Nilpotent Radical -- ยง 4. Basic Conventions. Elementary Combinatorics -- ยง 5. The Method of Sandwiches -- ยง 6. Filtrations in Lie Algebras -- ยง 7. Main results and Structure of Proofs -- ยง 8. Commentary -- 2 The Descent to Sandwiches -- ยง 1. Descent to nil-elements of index 3 -- ยง 2. Descent to Thin Sandwiches (General Case) -- ยง 3. Descent to Thin Sandwiches (the Case p >> n) -- ยง 4. Descent from C2* to C(p-3)/2* 41 -- ยง 5. Commentary -- 3 Local Analysis on Thin Sandwiches -- ยง 1. A First Footbridge Between Thin and Thick Sandwiches -- ยง 2. A Second Footbridge Between Thin and Thick Sandwiches -- ยง 3. Two Necessary Lemmas -- ยง 4. Sandwich Algebras -- ยง 5. Commentary -- 4 Proof of the Main Theorem -- ยง 1. Pairs of Thin Sandwiches -- ยง 2. Thick Pairs of Thin Sandwiches -- ยง 3. Completion of the Proof of the Main Theorem -- ยง 4. Commentary -- 5 Evolution of the Method of Sandwiches -- ยง 1. Rehabilitation of False Sandwiches -- ยง 2. A Geodesic Connecting Theorems 3.4.1 and 1.7.4 -- ยง 3. The Local Nilpotency of Sandwich Algebras -- ยง 4. The Sandwich Radical and its Applications -- ยง 5. Commentary -- 6 The Problem of Global Nilpotency -- ยง 1. The Nilpotency Class of a Lie Algebra with En -- ยง 2. Combination of Solubility and the Engel Condition En -- ยง 3. Insolubility for n Close to p -- ยง 4. Global Nilpotency for p >> n -- ยง 5. Commentary -- 7 Finite p-Groups and Lie Algebras -- ยง 1. Fundamental Relations Between Groups and Lie Algebras -- ยง 2. The Ideal of Relations (a general Survey) -- ยง 3. Multilinear Relations: Proofs of Theorems 2.3 and 2.4 -- ยง 4. Commentary -- Appendix I An Effective Version of the Proof of Theorem 1.7.4 in Terms of Recursive Functions (due to E. I. Zelโmanov) -- Appendix II A Short Biography of William Burnside (after A.R. Forsyth [52]) -- Epilogue -- Notes Added in Proof -- References -- Author Index -- Notation