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A Sampling of Remarkable Groups

Thompson's, Self-similar, Lamplighter, and Baumslag-Solitar

  • Marianna C. Bonanome
  • Margaret H. Dean
  • Judith Putnam Dean

Part of the Compact Textbooks in Mathematics book series (CTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean
    Pages 1-36
  3. Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean
    Pages 37-66
  4. Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean
    Pages 67-104
  5. Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean
    Pages 105-132
  6. Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean
    Pages 133-152
  7. Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean
    Pages 153-179
  8. Back Matter
    Pages 181-188

About this book

Introduction

This textbook offers students with a basic understanding of group theory a preview of several interesting groups they would not typically encounter until later in their academic careers. By presenting these advanced concepts at this stage, they will gain a deeper understanding of the subject and be motivated to explore more of it.

Groups covered include Thompson’s groups, self-similar groups, Lamplighter groups, and Baumslag-Solitar groups. Each chapter focuses on one of these groups, and begins by discussing why they are interesting, how they originated, and why they are important mathematically. A collection of specific references for additional reading, topics for further research, and exercises are included at the end of every chapter to encourage students’ continued education.

With its accessible presentation and engaging style, A Sampling of Remarkable Groups is suitable for students in upper-level undergraduate or beginning graduate abstract algebra courses. It will also be of interest to researchers in mathematics, computer science, and related fields.

Keywords

Baumslag-Solitar groups Lamplighter groups Thompson's group automatic groups braid groups Combinatorial group theory Geometric group theory self-similar groups amenability of groups dead-end depth Grigorchuk's group Tower of Hanoi

Authors and affiliations

  • Marianna C. Bonanome
    • 1
  • Margaret H. Dean
    • 2
  • Judith Putnam Dean
    • 3
  1. 1.Department of Math and Computer ScienceNew York City College of Technology, The City University of NewYorkBrooklynUSA
  2. 2.Department of MathematicsBorough of Manhattan Community College, The City University of New YorkNew YorkUSA
  3. 3.Department of MathematicsMonroe Community CollegeRochesterUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-01978-5
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-01976-1
  • Online ISBN 978-3-030-01978-5
  • Series Print ISSN 2296-4568
  • Series Online ISSN 2296-455X
  • Buy this book on publisher's site