Group Ring Groups Orders And Generic Constructions Of Units
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Group Ring Groups Orders and generic constructions of units
Author | : Eric Jespers,Ángel del Río |
Publsiher | : de Gruyter |
Total Pages | : 0 |
Release | : 2016 |
Genre | : Group rings |
ISBN | : 3110372789 |
Download Group Ring Groups Orders and generic constructions of units Book in PDF, Epub and Kindle
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.
Group Ring Groups
Author | : Eric Jespers,Ángel del Río |
Publsiher | : De Gruyter Textbook |
Total Pages | : 0 |
Release | : 2016 |
Genre | : Group rings |
ISBN | : 3110411490 |
Download Group Ring Groups Book in PDF, Epub and Kindle
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.
Orders and Generic Constructions of Units
Author | : Eric Jespers,Ángel del Río |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 459 |
Release | : 2015-11-13 |
Genre | : Mathematics |
ISBN | : 9783110372946 |
Download Orders and Generic Constructions of Units Book in PDF, Epub and Kindle
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.
Algorithmic and Experimental Methods in Algebra Geometry and Number Theory
Author | : Gebhard Böckle,Wolfram Decker,Gunter Malle |
Publsiher | : Springer |
Total Pages | : 753 |
Release | : 2018-03-22 |
Genre | : Mathematics |
ISBN | : 9783319705668 |
Download Algorithmic and Experimental Methods in Algebra Geometry and Number Theory Book in PDF, Epub and Kindle
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.
Structure Theorems of Unit Groups
Author | : Eric Jespers,Ángel del Río |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 227 |
Release | : 2015-11-13 |
Genre | : Mathematics |
ISBN | : 9783110411508 |
Download Structure Theorems of Unit Groups Book in PDF, Epub and Kindle
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.
Group Theory and Computation
Author | : N.S. Narasimha Sastry,Manoj Kumar Yadav |
Publsiher | : Springer |
Total Pages | : 206 |
Release | : 2018-09-21 |
Genre | : Mathematics |
ISBN | : 9789811320477 |
Download Group Theory and Computation Book in PDF, Epub and Kindle
This book is a blend of recent developments in theoretical and computational aspects of group theory. It presents the state-of-the-art research topics in different aspects of group theory, namely, character theory, representation theory, integral group rings, the Monster simple group, computational algorithms and methods on finite groups, finite loops, periodic groups, Camina groups and generalizations, automorphisms and non-abelian tensor product of groups. Presenting a collection of invited articles by some of the leading and highly active researchers in the theory of finite groups and their representations and the Monster group, with a focus on computational aspects, this book is of particular interest to researchers in the area of group theory and related fields of mathematics.
Complementation of Normal Subgroups
Author | : Joseph Kirtland |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 156 |
Release | : 2017-09-11 |
Genre | : Mathematics |
ISBN | : 9783110480214 |
Download Complementation of Normal Subgroups Book in PDF, Epub and Kindle
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
Structure Theorems of Unit Groups
Author | : Eric Jespers,Ángel del Río |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 227 |
Release | : 2015-11-13 |
Genre | : Mathematics |
ISBN | : 9783110412758 |
Download Structure Theorems of Unit Groups Book in PDF, Epub and Kindle
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.