Contents ix §10.1. Sets of bounded doubling 220 §10.2. Polynomial growth 223 §10.3. Fundamental groups of compact manifolds (optional) 225 §10.4. A Margulis-type lemma 229 Part 2. Related Articles Chapter 11. The Jordan-Schur theorem 233 §11.1. Proofs 234 Chapter 12. Nilpotent groups and nilprogressions 237 §12.1. Some elementary group theory 239 §12.2. Nilprogressions 244 Chapter 13. Ado’s theorem 249 §13.1. The nilpotent case 252 §13.2. The solvable case 254 §13.3. The general case 258 Chapter 14. Associativity of the Baker-Campbell-Hausdorff-Dynkin law 259 Chapter 15. Local groups 265 §15.1. Lie’s third theorem 269 §15.2. Globalising a local group 270 §15.3. A nonglobalisable group 274 Chapter 16. Central extensions of Lie groups, and cocycle averaging 277 §16.1. A little group cohomology 279 §16.2. Proof of theorem 285 Chapter 17. The Hilbert-Smith conjecture 289 §17.1. Periodic actions of prime order 290 §17.2. Reduction to the p-adic case 293 Chapter 18. The Peter-Weyl theorem and nonabelian Fourier analysis 297 §18.1. Proof of the Peter-Weyl theorem 298 §18.2. Nonabelian Fourier analysis 302 Chapter 19. Polynomial bounds via nonstandard analysis 307 Chapter 20. Loeb measure and the triangle removal lemma 313
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