Topics in Geometric Group TheoryIn this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields. |
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Obsah
Introduction | 1 |
Free products and free groups | 17 |
Finitelygenerated groups | 43 |
Finitelygenerated groups viewed as metric spaces Ðને ઝે | 75 |
Finitelypresented groups | 117 |
Growth of finitelygenerated groups | 151 |
Groups of exponential or polynomial growth | 187 |
The first Grigorchuk group | 211 |
| 265 | |
| 295 | |
Další vydání - Zobrazit všechny
Běžně se vyskytující výrazy a sousloví
abelian action acts Algebra appears argument assume automorphism Cayley graph Chapter Check Claim closed commensurable compact Complement complex compute connected consequence Consider constant contains Corollary corresponding covering curvature cyclic defined Definition denote dimension discrete Editors element ends equivalent example Exercise exists exponential growth fact finite group finite index finitely presented finitely-generated group finitely-presented follows free group free product fundamental group geometric given growth function growth series homomorphism hyperbolic groups infinite integer isometries isomorphic Item known lattice Lemma length Lie group linear manifold mapping Math metric space natural nilpotent normal subgroup Observe pair particular precisely problem proof properties Proposition quasi-isometric quotient rank Recall reduced relations respectively result Riemannian sense sequence shown simple space subgroup of finite subset surface Theorem topology tree University vertex vertices
Oblíbené pasáže
Strana 278 - G. HIGMAN, Unrestricted free products and varieties of topological groups, J. London Math. Soc. 27(1952), 73-81. 12. ST Hu, "Homotopy Theory," Academic Press, New York/London, 1959. 13. AG KUROSH, "The Theory of Groups,
Strana 280 - On everywhere dense imbedding of free groups in Lie groups, Nagoya Math.
Strana 278 - Subgroups of finitely presented groups. Proc. Royal Soc. London Ser. A 262, 455-475 (1961).
Strana 277 - P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. 4 (1954), 419-436.
Strana 272 - Geodesic automation and growth functions for Artin groups of finite type, Math. Ann. 301 (1995), 307-324.
Odkazy na tuto knihu
Bibliografické údaje
| Název | Topics in Geometric Group Theory Chicago Lectures in Mathematics, ISSN 0069-3286 |
| Autor | Pierre de la Harpe |
| Vydání | ilustrované vydání |
| Vydavatel | University of Chicago Press, 2000 |
| ISBN | 0226317196, 9780226317199 |
| Délka | Počet stran: 310 |
| Exportovat citaci | BiBTeX EndNote RefMan |