Lectures on Finitely Generated Solvable Groups by Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman. [delta]

Format:

Book

Author/Creator:

Bencsath, Katalin A.

Contributor:

Bonanome, Marianna C.

Dean, Margaret H.

Zyman, Marcos

Series:

SpringerBriefs in mathematics

SpringerBriefs in Mathematics,

Language:

English

Subjects (All):

Mathematics.

Algebra.

Group theory.

Combinatorial analysis.

applied mathematics.

mathematics.

algebra.

Physical Description:

1 online resource

Place of Publication:

New York, NY Springer New York Imprint Springer 2013

System Details:

text file PDF

Summary:

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; thereforethese 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 froma combinatorial group theory perspective

Contents:

Foreword

Preface.- Preliminaries.- Tools: Presentations and their Calculus.- Constructions

Representations andaTheorem 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

Notes:

Includes bibliographical references

ISBN:

9781461454502

1461454506

9781461454496

1461454492

OCLC:

1245509555

Access Restriction:

Restricted for use by site license