Lectures on Finitely Generated Solvable Groups - Brossura

Bencsath, Katalin A. A.

Brossura

ISBN 10: 1461454492 ISBN 13: 9781461454496

Casa editrice: Springer, 2012

Riassunto

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".

Su questo libro

Recensione

From the reviews:

“This work by Bencsáth (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)

Contenuti

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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461454492
• ISBN 13: 9781461454496
• Rilegatura: Copertina flessibile
• Numero di pagine: 68
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania