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Groups, Graphs and Trees
An Introduction to the Geometry of Infinite Groups

$42.00 USD

Part of London Mathematical Society Student Texts

  • Author: John Meier, Lafayette College, Pennsylvania
  • Date Published: September 2008
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511421594

$ 42.00 USD
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  • 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. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.

    • Only prerequisite is one semester of abstract algebra: accessible to undergraduate and beginning graduate students
    • Over 150 exercises and 95 figures aid understanding and develop geometric intuition
    • Modern approach with many contemporary results presented
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    Reviews & endorsements

    'Meier has the rare ability to make complex concepts accessible to novices while simultaneously challenging the experienced. … With well-chosen illustrations and examples, Meier succeeds brilliantly in this unique approach.' SciTech Book News

    '… totally accessible to undergraduate students and would be a good textbook for an advanced undergraduate course in group theory, or a graduate course in geometric group theory.' Mathematical Review

    '… an excellent introduction to geometric group theory. … Carefully chosen examples are an essential part of the exposition and they really help to understand general constructions.' EMS Newsletter

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    Product details

    • Date Published: September 2008
    • format: Adobe eBook Reader
    • isbn: 9780511421594
    • contains: 1 table 175 exercises
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface
    1. Cayley's theorems
    2. Groups generated by reflections
    3. Groups acting on trees
    4. Baumslag-Solitar groups
    5. Words and Dehn's word problem
    6. A finitely-generated, infinite, Torsion group
    7. Regular languages and normal forms
    8. The Lamplighter group
    9. The geometry of infinite groups
    10. Thompson's group
    11. The large-scale geometry of groups
    Bibliography
    Index.

  • Author

    John Meier, Lafayette College, Pennsylvania
    John Meier is a Professor in the Department of Mathematics at Lafayette College.

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