Overview
- Includes a foreword by Gilbert Baumslag, a world renowned expert in combinatorial group theory
- Serves as a field guide to the class of finitely generated solvable groups from a combinatorial group theory perspective
- Provides examples to help illustrate key concepts
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (7 chapters)
Keywords
About this book
Lectures on Finitely Generated Solvable Groups are based on the “Topics in Group Theory" course focused on finitely generated solvable groups that was given by Gilbert G. Baumslag at the Graduate School and University Center of the City University of New York. While knowledge about finitely generated nilpotent groups is extensive, much less is known about the more general class of solvable groups containing them. The study of finitely generated solvable groups involves many different threads; therefore these notes contain discussions on HNN extensions; amalgamated and wreath products; and other concepts from combinatorial group theory as well as commutative algebra. Along with Baumslag’s Embedding Theorem for Finitely Generated Metabelian Groups, two theorems of Bieri and Strebel are presented to provide a solid foundation for understanding the fascinating class of finitely generated solvable groups. Examples are also supplied, which help illuminate many of the key concepts contained in the notes. Requiring only a modest initial group theory background from graduate and post-graduate students, these notes provide a field guide to the class of finitely generated solvable groups from a combinatorial group theory perspective.
Reviews
From the reviews:
“This work by Bencsáth (Manhattan College) and CUNY colleagues begins with 25 pages of combinatorial group theory preliminaries … . Recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 50 (8), April, 2013)Authors and Affiliations
Bibliographic Information
Book Title: Lectures on Finitely Generated Solvable Groups
Authors: Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-1-4614-5450-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman 2013
Softcover ISBN: 978-1-4614-5449-6Published: 29 October 2012
eBook ISBN: 978-1-4614-5450-2Published: 28 October 2012
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XIV, 52
Topics: Group Theory and Generalizations, Combinatorics, Algebra, General Algebraic Systems, Commutative Rings and Algebras