04666nam 22007815 450 991043814850332120220415200421.01-283-90905-71-4614-5450-610.1007/978-1-4614-5450-2(CKB)2670000000278243(EBL)1081924(OCoLC)818827923(SSID)ssj0000799759(PQKBManifestationID)11497649(PQKBTitleCode)TC0000799759(PQKBWorkID)10765056(PQKB)10348419(DE-He213)978-1-4614-5450-2(MiAaPQ)EBC1081924(PPN)16830306X(EXLCZ)99267000000027824320121029d2013 u| 0engur|n|---|||||txtccrLectures on finitely generated solvable groups[electronic resource] /by Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman1st ed. 2013.New York, NY :Springer New York :Imprint: Springer,2013.1 online resource (62 p.)SpringerBriefs in Mathematics,2191-8198Description based upon print version of record.1-4614-5449-2 Includes bibliographical references.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.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.SpringerBriefs in Mathematics,2191-8198Group theoryCombinatoricsAlgebraCommutative algebraCommutative ringsGroup Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Combinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000General Algebraic Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/M1106XCommutative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11043Group theory.Combinatorics.Algebra.Commutative algebra.Commutative rings.Group Theory and Generalizations.Combinatorics.Algebra.General Algebraic Systems.Commutative Rings and Algebras.515.7242Bencsath Katalin Aauthttp://id.loc.gov/vocabulary/relators/aut1061366Bonanome Marianna Cauthttp://id.loc.gov/vocabulary/relators/autDean Margaret Hauthttp://id.loc.gov/vocabulary/relators/autZyman Marcosauthttp://id.loc.gov/vocabulary/relators/autBOOK9910438148503321Lectures on Finitely Generated Solvable Groups2518593UNINA