Lectures on Finitely Generated Solvable Groups
By: by Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman
Contributors: Bonanome, Marianna C.; Dean, Margaret H.; Zyman, Marcos; SpringerLink (Online service)
Series: SpringerBriefs in Mathematics
Publisher: Springer New York; Imprint: Springer
Published: 2013
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 52
ISBN-13: 9781461454502
Subjects: Group theory; Group Theory and Generalizations; Commutative Rings and Algebras; Algebra; Mathematics; General Algebraic Systems; Combinatorial analysis
Description: <p><i>Lectures on Finitely Generated Solvable Groups</i> 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.​</p>
Table of contents: title: Foreword; title: Preface.-  Preliminaries.-  Tools: Presentations and their Calculus.-  Constructions; title: Representations and a Theorem of Krasner and Kaloujnine.- The Bieri-Strebel Theorems; title: Finitely Generated Metabelian Groups; title: An Embedding Theorem for Finitely Generated Metabelian Groups​.- Sketch of Proof of Lemma 1.1; title: Theorem 2.1 Details; title: Presenting an (Internal) HNN-Extension; title: References.