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## Details

Material Type: | Internet resource |
---|---|

Document Type: | Book, Internet Resource |

All Authors / Contributors: |
Pierre de La Harpe |

ISBN: | 0226317196 9780226317199 0226317218 9780226317212 |

OCLC Number: | 43227307 |

Description: | vi, 310 pages : illustrations ; 24 cm. |

Contents: | Gauss' circle problem and Polya's random walks on lattices -- The circle problem -- Polya's recurrence theorem -- Free products and free groups -- Free Products of Groups -- The Table-Tennis Lemma (Klein's criterion) and examples of free products -- Finitely-generated groups -- Finitely-generated and infinitely-generated groups -- Uncountably many groups with two generators (B.H. Neumann's method) -- On groups with two generators -- On finite quotients of the modular group -- Finitely-generated groups viewed as metric spaces -- Word lengths and Cayley graphs -- Quasi-isometries -- Finitely-presented groups -- Finitely-presented groups -- The Poincare theorem on fundamental polygons -- On fundamental groups and curvature in Riemannian geometry -- Complement on Gromov's hyperbolic groups -- Growth of finitely-generated groups -- Growth functions and growth series of groups -- Generalities on growth types -- Exponential growth rate and entropy -- Groups of exponential or polynomial growth -- On groups of exponential growth -- On uniformly exponential growth -- On groups of polynomial growth -- Complement on other kinds of growth -- The first Grigorchuk group -- Rooted d-ary trees and their automorphisms -- The group [Gamma] as an answer to one of Burnside's problems -- On some subgroups of [Gamma] -- Congruence subgroups -- Word problem and non-existence of finite presentations -- Growth -- Exercises and complements. |

Series Title: | Chicago lectures in mathematics. |

Responsibility: | Pierre de la Harpe. |

More information: |

### Abstract:

This work seeks to offer a concise introduction to geometric group theory - a method for studying infinite groups via their intrinsic geometry. Basic combinatorial and geometric group theory is presented, along with research on the growth of groups, and exercises and problems.
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