Topics in groups and geometry growth, amenability, and random walks - Ceccherini-Silberstein, Tullio 1966-; D'Adderio, Michele (Springer International Publishing, 2021)
- Foreword -- Preface -- Part I Algebraic Theory: 1. Free Groups -- 2. Nilpotent Groups -- 3. Residual Finiteness and the Zassenhaus Filtration -- 4. Solvable Groups -- 5. Polycyclic Groups -- 6. The Burnside Problem -- Part II Geometric Theory: 7. Finitely Generated Groups and Their Growth Functions -- 8. Hyperbolic Plane Geometry and the Tits Alternative -- 9. Topological Groups, Lie Groups, and Hilbert Fifth Problem -- 10. Dimension Theory -- 11. Ultraﬁlters, Ultraproducts, Ultrapowers, and Asymptotic Cones -- 12. Gromov’s Theorem -- Part III Analytic and Probabilistic Theory: 13. The Theorems of Polya and Varopoulos -- 14. Amenability, Isoperimetric Proﬁle, and Følner Functions -- 15. Solutions or Hints to Selected Exercises -- References -- Subject Index -- Index of Authors
Keywords: Group theory; Associative rings; Rings (Algebra); Geometry; Probabilities; Graph theory