A Sampling of Remarkable Groups

1. Front Matter

   Pages i-xii

   PDF

2. Preliminaries

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

   Pages 1-36

3. Thompson’s Group F

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

   Pages 37-66

4. Self-Similar Groups

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

   Pages 67-104

5. The Lamplighter Group L₂

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

   Pages 105-132

6. Baumslag–Solitar Groups

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

   Pages 133-152

7. Solutions

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

   Pages 153-179

8. Back Matter

   Pages 181-188

   PDF

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.

• 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

“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)

• Department of Math and Computer Science, New York City College of Technology, The City University of NewYork, Brooklyn, USA

  Marianna C. Bonanome

• Department of Mathematics, Borough of Manhattan Community College, The City University of New York, New York, USA

  Margaret H. Dean

• Department of Mathematics, Monroe Community College, Rochester, USA

  Judith Putnam Dean

​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. 

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