Topics in Geometric Group Theory

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University of Chicago Press, Oct 15, 2000 - Mathematics - 310 pages
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In 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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Free products and free groups
HI Finitelygenerated groups
Finitelygenerated groups viewed as metric spaces
Finitelypresented groups
Growth of finitelygenerated groups
Groups of exponential or polynomial growth
The first Grigorchuk group
Index of research problems

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Page 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,
Page 280 - On everywhere dense imbedding of free groups in Lie groups, Nagoya Math.
Page 278 - Subgroups of finitely presented groups. Proc. Royal Soc. London Ser. A 262, 455-475 (1961).
Page 277 - P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. 4 (1954), 419-436.
Page 272 - Geodesic automation and growth functions for Artin groups of finite type, Math. Ann. 301 (1995), 307-324.

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About the author (2000)

Pierre de la Harpe is a professor of mathematics at the Université de Genève, Switzerland. He is the author, coauthor, or coeditor of several books, including La propriété (T) de Kazhdan pour les groupes localement compacts and Sur les groupes hyperboliques d'après Mikhael Gromov.

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