A Sampling of Remarkable Groups: Thompson's, Self-similar, Lamplighter, and Baumslag-Solitar

Description

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. Front Matter ....Pages i-xii Preliminaries (Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean)....Pages 1-36 Thompson’s Group F (Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean)....Pages 37-66 Self-Similar Groups (Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean)....Pages 67-104 The Lamplighter Group L2 (Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean)....Pages 105-132 Baumslag–Solitar Groups (Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean)....Pages 133-152 Solutions (Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean)....Pages 153-179 Back Matter ....Pages 181-188