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Lectures on Finitely Generated Solvable Groups
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Catalogue Information
Field name
Details
Dewey Class
512.2
Title
Lectures on Finitely Generated Solvable Groups (EB) / by Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman.
Author
Bencsath, Katalin A.
Added Personal Name
Bonanome, Marianna C.
Dean, Margaret H.
Zyman, Marcos
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : Springer
, 2013.
Physical Details
XIV, 52 pages : online resource.
Series
SpringerBriefs in Mathematics
2191-8198
ISBN
9781461454502
Summary Note
Lectures on Finitely Generated Solvable Groups are based on the âTopics 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 Baumslagâs 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.:
Contents note
Foreword -- 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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
http://dx.doi.org/10.1007/978-1-4614-5450-2
Links to Related Works
Subject References:
Algebra
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Combinatorics
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Commutative Rings and Algebras
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General Algebraic Systems
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Group theory
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Group Theory and Generalizations
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Mathematics
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Authors:
author
.
Bencsath, Katalin A.
.
Bonanome, Marianna C.
.
Dean, Margaret H.
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Zyman, Marcos
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Corporate Authors:
SpringerLink (Online service)
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Series:
SpringerBriefs in Mathematics
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Classification:
512.2
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