Title Lectures on Finitely Generated Solvable Groups / by Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman. : [delta]

Published New York, NY : Springer New York : Imprint : Springer, 2013

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Description 1 online resource Series SpringerBriefs in Mathematics, SpringerBriefs in mathematics. Contents Foreword -- Preface.- Preliminaries.- Tools: Presentations and their Calculus.- Constructions -- Representations andaTheorem of Krasner and Kaloujnine.-The Bieri-Strebel Theorems -- Finitely Generated Metabelian Groups -- An Embedding Theorem for Finitely Generated Metabelian Groups .-Sketch of Proof of Lemma 1.1 -- Theorem 2.1 Details -- Presenting an (Internal) HNN-Extension -- References Summary 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; thereforethese 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 froma combinatorial group theory perspective Bibliography Includes bibliographical references Subject Mathematics. Algebra. Group theory. Combinatorial analysis. applied mathematics. mathematics. algebra. Matemáticas Álgebra Teoría de grupos Análisis combinatorio Algebra Combinatorial analysis Group theory Mathematics Form Electronic book Author Bonanome, Marianna C Dean, Margaret H Zyman, Marcos ISBN 9781461454502 1461454506 9781461454496 1461454492

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