# Groups Graphs And Trees An Introduction To The Geometry Of Infinite Groups Pdf

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Algebra IV pp Cite as. The achievements of Galois theory stimulated intensive study of permutation groups, and indeed in the early stages of its development, group theory was preoccupied almost exclusively with finite groups. However, under the influence of geometry, topology, and the theory of differential equations, there arose a pressing need to consider infinite groups of transformations.

## Groups, Graphs and Trees - Ebook

Niels Lauritzen, Concrete abstract algebra Chapter 2 or any textbook on introductory group theory. Laurent Bartholdi, Growth of groups and wreath products an expanded version of a mini-course given at "Le Louverain", June , Brian Bowditch, A course on geometric group theory , Marc Culler, Notes on free groups , Steve Gersten, Introduction to hyperbolic and automatic groups , Notes from the Banff conference,

Groups, Graphs and Trees is an introduction to geometric group theory. Assuming some acquaintance with the fundamentals of group theory e. Then, the structure of the group can be read on the structure of the corresponding graph. The effectiveness of this point of view is clearly illustrated at many places throughout the book; geometric group theory provides clear and illustrative proofs of many difficult results especially for finitely generated groups. It is a beautiful and modern approach to the study of infinite groups, and it deepens the understanding of many abstract algebraic problems.

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MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Some other sources. Very easy to read and covers a lot of ground. Another classic, but in French. If you look around the web, you can find English translations.

Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored.