Structure Theorems Of Unit Groups

Author : Eric Jespers,Ángel del Río
Publisher : Walter de Gruyter GmbH & Co KG
Page : 227 pages
File Size : 51,9 Mb
Release : 2015-11-13
Category : Mathematics
ISBN : 9783110412758

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Structure Theorems of Unit Groups by Eric Jespers,Ángel del Río Pdf

This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.

Author : Eric Jespers,Ángel del Río
Publisher : Walter de Gruyter GmbH & Co KG
Page : 227 pages
File Size : 49,5 Mb
Release : 2015-11-13
Category : Mathematics
ISBN : 9783110411508

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Structure Theorems of Unit Groups by Eric Jespers,Ángel del Río Pdf

This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.

Author : Eric Jespers,Ángel del Río
Publisher : De Gruyter Textbook
Page : 0 pages
File Size : 44,5 Mb
Release : 2016
Category : Group rings
ISBN : 3110411490

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Group Ring Groups by Eric Jespers,Ángel del Río Pdf

This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.

Author : Eric Jespers,Ángel del Río
Publisher : de Gruyter
Page : 0 pages
File Size : 45,5 Mb
Release : 2016
Category : Group rings
ISBN : 3110372789

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Group Ring Groups: Orders and generic constructions of units by Eric Jespers,Ángel del Río Pdf

This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.

Author : Vesselin Drensky
Publisher : CRC Press
Page : 328 pages
File Size : 53,6 Mb
Release : 2021-02-28
Category : Mathematics
ISBN : 9781000657357

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Methods in Ring Theory by Vesselin Drensky Pdf

"Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."

Author : Eric Jespers,Ángel del Río
Publisher : Walter de Gruyter GmbH & Co KG
Page : 459 pages
File Size : 48,5 Mb
Release : 2015-11-13
Category : Mathematics
ISBN : 9783110372946

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Orders and Generic Constructions of Units by Eric Jespers,Ángel del Río Pdf

This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.

Author : Gebhard Böckle,Wolfram Decker,Gunter Malle
Publisher : Springer
Page : 753 pages
File Size : 53,9 Mb
Release : 2018-03-22
Category : Mathematics
ISBN : 9783319705668

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Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory by Gebhard Böckle,Wolfram Decker,Gunter Malle Pdf

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 44,6 Mb
Release : 2007-05-23
Category : Mathematics
ISBN : 9780387499222

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Number Theory by Henri Cohen Pdf

The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.

Author : Xiao Chen
Publisher : Unknown
Page : 146 pages
File Size : 55,5 Mb
Release : 1997
Category : Electronic
ISBN : UVA:X004142979

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Unit Groups of P-adic Group Rings by Xiao Chen Pdf

Author : Joseph Kirtland
Publisher : Walter de Gruyter GmbH & Co KG
Page : 156 pages
File Size : 42,8 Mb
Release : 2017-09-11
Category : Mathematics
ISBN : 9783110480214

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Complementation of Normal Subgroups by Joseph Kirtland Pdf

Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations. Contents Prerequisites The Schur-Zassenhaus theorem: A bit of history and motivation Abelian and minimal normal subgroups Reduction theorems Subgroups in the chief series, derived series, and lower nilpotent series Normal subgroups with abelian sylow subgroups The formation generation Groups with specific classes of subgroups complemented

Author : Michel Brion,Shrawan Kumar
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 52,9 Mb
Release : 2007-08-08
Category : Mathematics
ISBN : 9780817644055

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Frobenius Splitting Methods in Geometry and Representation Theory by Michel Brion,Shrawan Kumar Pdf

Systematically develops the theory of Frobenius splittings and covers all its major developments. Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings—definitions, properties and examples—to cutting edge research.

Author : Karl H. Hofmann,Sidney A. Morris
Publisher : Unknown
Page : 1034 pages
File Size : 45,7 Mb
Release : 2020-06-08
Category : Compact groups
ISBN : 3110695952

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The Structure of Compact Groups by Karl H. Hofmann,Sidney A. Morris Pdf

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Author : Frank Olaf Wagner
Publisher : Cambridge University Press
Page : 326 pages
File Size : 42,6 Mb
Release : 1997-08-21
Category : Mathematics
ISBN : 0521598397

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Stable Groups by Frank Olaf Wagner Pdf

In this book the general theory of stable groups is developed from the beginning.

Author : Anton Deitmar,Siegfried Echterhoff
Publisher : Springer
Page : 330 pages
File Size : 47,9 Mb
Release : 2014-06-21
Category : Mathematics
ISBN : 9783319057927

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Principles of Harmonic Analysis by Anton Deitmar,Siegfried Echterhoff Pdf

This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

Author : Donald S. Passman,William Chin,James Osterburg,Declan Patrick Francis Quinn
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 49,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839041

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Groups, Rings and Algebras by Donald S. Passman,William Chin,James Osterburg,Declan Patrick Francis Quinn Pdf

This is a companion volume to the conference in honor of Donald S. Passman held in Madison, Wisconsin in June 2005. It contains research papers on Algebras, Group Rings, Hopf Algebras, Invariant Theory, Lie Algebras and their Enveloping Algebras, Noncommutative Algebraic Geometry, Noncommutative Rings, and other topics. The papers represent an important part of the latest research in these areas.