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© 2018

A Sampling of Remarkable Groups

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

Textbook

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

  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

About the authors

​Dr. Marianna Bonanome is an associate professor in mathematics at City Tech, CUNY.  Her current research interest is in quantum algorithms and combinatorial group theory. She coordinates a faculty seminar on teaching best practices, is writing intensive certified and experiments with new ways of using technology in the classroom.

Dr. Margaret H. Dean is an associate professor in mathematics at BMCC, CUNY.  Her current research interest is in metabelian groups.  In the area of undergraduate education, she is involved in various projects to study, disseminate and implement alternative learning methods in the classroom and to promote quantitative literacy across the curriculum.

Judith Putnam Dean is an associate professor in mathematics at Monroe Community College. As a Flipped Learning specialist, she helped develop a mastery flipped program for developmental math, designs flipped classes for upper level courses, creates instructional videos and shares her expertise through leading workshops. In addition she has created online, OER and writing intensive courses. 

Bibliographic information

  • Book Title A Sampling of Remarkable Groups
  • Book Subtitle Thompson's, Self-similar, Lamplighter, and Baumslag-Solitar
  • Authors Marianna C. Bonanome
    Margaret H. Dean
    Judith Putnam Dean
  • Series Title Compact Textbooks in Mathematics
  • Series Abbreviated Title Compact Textbooks in Mathematics
  • 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 Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-030-01976-1
  • eBook ISBN 978-3-030-01978-5
  • Series ISSN 2296-4568
  • Series E-ISSN 2296-455X
  • Edition Number 1
  • Number of Pages XII, 188
  • Number of Illustrations 157 b/w illustrations, 13 illustrations in colour
  • Topics Group Theory and Generalizations
  • Buy this book on publisher's site

Reviews

“This delightful book is dedicated to introducing an advanced undergraduate student to the study of some aspects of infinite groups theory. … The whole book is enriched with beautiful and instructive illustrations.” (Enrico Jabara, zbMATH 1446.20001, 2020)