Lectures On Finitely Generated Solvable Groups
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Lectures On Finitely Generated Solvable Groups
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Author : Katalin A. Bencsath
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-28
Lectures On Finitely Generated Solvable Groups written by Katalin A. Bencsath and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-28 with Mathematics categories.
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.
Lectures On Finitely Generated Solvable Groups
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Author : Springer
language : en
Publisher:
Release Date : 2012-10-29
Lectures On Finitely Generated Solvable Groups written by Springer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-29 with categories.
Lectures On Profinite Topics In Group Theory
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Author : Benjamin Klopsch
language : en
Publisher: Cambridge University Press
Release Date : 2011-02-10
Lectures On Profinite Topics In Group Theory written by Benjamin Klopsch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-10 with Mathematics categories.
In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.
The Theory Of Infinite Soluble Groups
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Author : John C. Lennox
language : en
Publisher: Clarendon Press
Release Date : 2004-08-19
The Theory Of Infinite Soluble Groups written by John C. Lennox and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-19 with Mathematics categories.
The central concept in this monograph is that of a soluble group - a group which is built up from abelian groups by repeatedly forming group extensions. It covers all the major areas, including finitely generated soluble groups, soluble groups of finite rank, modules over group rings, algorithmic problems, applications of cohomology, and finitely presented groups, whilst remaining fairly strictly within the boundaries of soluble group theory. An up-to-date survey of the area aimed at research students and academic algebraists and group theorists, it is a compendium of information that will be especially useful as a reference work for researchers in the field.
Lectures On Subgroups Of Sylow Type In Finite Soluble Groups
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Author : Wolfgang Gaschütz
language : en
Publisher:
Release Date : 1979
Lectures On Subgroups Of Sylow Type In Finite Soluble Groups written by Wolfgang Gaschütz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Computational And Combinatorial Group Theory And Cryptography
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Author : Benjamin Fine
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Computational And Combinatorial Group Theory And Cryptography written by Benjamin Fine and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.
This volume contains the proceedings of the AMS Special Session on Computational Algebra, Groups, and Applications, held April 30-May 1, 2011, at the University of Nevada, Las Vegas, Nevada, and the AMS Special Session on the Mathematical Aspects of Cryptography and Cyber Security, held September 10-11, 2011, at Cornell University, Ithaca, New York. Over the past twenty years combinatorial and infinite group theory has been energized by three developments: the emergence of geometric and asymptotic group theory, the development of algebraic geometry over groups leading to the solution of the Tarski problems, and the development of group-based cryptography. These three areas in turn have had an impact on computational algebra and complexity theory. The papers in this volume, both survey and research, exhibit the tremendous vitality that is at the heart of group theory in the beginning of the twenty-first century as well as the diversity of interests in the field.
Characters And Blocks Of Solvable Groups
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Author : James Cossey
language : en
Publisher: Springer Nature
Release Date :
Characters And Blocks Of Solvable Groups written by James Cossey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
A Sampling Of Remarkable Groups
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Author : Marianna C. Bonanome
language : en
Publisher: Springer
Release Date : 2019-01-05
A Sampling Of Remarkable Groups written by Marianna C. Bonanome and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-05 with Mathematics categories.
This textbook offers students with a basic understanding of group theory a preview of several interesting groups they would not typically encounter until later in their academic careers. By presenting these advanced concepts at this stage, they will gain a deeper understanding of the subject and be motivated to explore more of it. Groups covered include Thompson’s groups, self-similar groups, Lamplighter groups, and Baumslag-Solitar groups. Each chapter focuses on one of these groups, and begins by discussing why they are interesting, how they originated, and why they are important mathematically. A collection of specific references for additional reading, topics for further research, and exercises are included at the end of every chapter to encourage students’ continued education. With its accessible presentation and engaging style, A Sampling of Remarkable Groups is suitable for students in upper-level undergraduate or beginning graduate abstract algebra courses. It will also be of interest to researchers in mathematics, computer science, and related fields.
Nilpotent Groups
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Author : Philip Hall
language : en
Publisher:
Release Date : 1979
Nilpotent Groups written by Philip Hall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Algebra, Universal categories.
Representations Of Solvable Groups
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Author : Olaf Manz
language : en
Publisher: Cambridge University Press
Release Date : 1993-09-16
Representations Of Solvable Groups written by Olaf Manz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-16 with Mathematics categories.
Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtained can then be applied to infinite modules, and in particular to character theory (ordinary and Brauer) of solvable groups. The authors include proofs of Brauer's height zero conjecture and the Alperin-McKay conjecture for solvable groups. Gluck's permutation lemma and Huppert's classification of solvable two-transive permutation groups, which are essentially results about finite modules of finite groups, play important roles in the applications and a new proof is given of the latter. Researchers into group theory, representation theory, or both, will find that this book has much to offer.