Lectures on Finitely Generated Solvable Groups (eBook)

Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman (Autoren)

eBook Download: PDF

2012 | 2013
XIV, 52 Seiten
Springer New York (Verlag)
978-1-4614-5450-2 (ISBN)

Infos

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.​

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Lectures on Finitely Generated Solvable Groups are based on the "e;Topics in Group Theory"e; 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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 28.10.2012
• Reihe/Serie: SpringerBriefs in Mathematics
• Reihe/Serie: SpringerBriefs in Mathematics
• Zusatzinfo: XIV, 52 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• Themenwelt: Technik
• Schlagworte: amalgamated and wreath products • Baumslag embedding theorem • Bieri-Strebel theorems • Combinatorial group theory • combinatorics • finitely generated solvable groups • nilpotent, polycyclic, and metabelian groups
• ISBN-10: 1-4614-5450-6 / 1461454506
• ISBN-13: 978-1-4614-5450-2 / 9781461454502