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Overview"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." Full Product DetailsAuthor: Katalin A. Bencsath , Marianna C. Bonanome , Margaret H. Dean , Marcos ZymanPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 2013 ed. Dimensions: Width: 15.50cm , Height: 0.30cm , Length: 23.50cm Weight: 1.182kg ISBN: 9781461454496ISBN 10: 1461454492 Pages: 52 Publication Date: 29 October 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsForeword.- Preface.- Preliminaries.- Tools: Presentations and their Calculus.- Constructions.- Representations and a Theorem 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.ReviewsFrom the reviews: This work by Bencsath (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) From the reviews: This work by Bencsath (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) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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