Characters Of Groups And Lattices Over Orders
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Characters Of Groups And Lattices Over Orders
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Author : Alexander Zimmermann
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-01-19
Characters Of Groups And Lattices Over Orders written by Alexander Zimmermann and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-19 with Mathematics categories.
This is the fi rst textbook leading coherently from classical character theory to the theory of lattices over orders and integral representations of fi nite groups. Character theory is developed in a highly pedagogical way including many examples and exercises covering at once the fi rst defi nitions up to Clifford theory, Brauer’s induction theorem and the splitting fi eld theorem, as well as self-dual simple modules allowing bilinear forms. This latter part is done step by step using the approach given by Sin and Willems. Dirichlet characters and Dirichlet’s result on primes in arithmetic progressions are given as an application. Examples of integral representations of fi nite groups are already detailed at a quite early stage where appropriate, so that the more systematic treatment of lattices over orders is natural. After that, the necessary number theory and homological algebra is developed as far as needed. Maximal as well as hereditary orders are introduced and the Auslander- Buchsbaum theorem is proved. The Jordan-Zassenhaus theorem on the fi niteness of lattices in a given vector space is fully proved. Then the development and properties of class groups of orders is a fi rst focus. As a further highlight Swan’s example of a stably free but not free ideal over the integral group ring of the generalised quaternion group of order 32 is developed in great detail. A student friendly introduction to ordinary representation theory Many examples and exercises, including solutions for some of them, make the book well suited for self-study Leads coherently from ordinary character theory to the integral representation theory of lattices over orders Several topics appear for the fi rst time in a textbook, such as Sin-Willems’ approach to self-dual simple modules and Swan‘s example of a stably free non free ideal.
Lattices Over Orders I
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Author : Klaus W. Roggenkamp
language : en
Publisher: Springer
Release Date : 2006-11-15
Lattices Over Orders I written by Klaus W. Roggenkamp and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Lattices Over Orders
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Author : Klaus W. Roggenkamp
language : en
Publisher:
Release Date : 1970
Lattices Over Orders written by Klaus W. Roggenkamp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Lattice theory categories.
Representation Theory Of Finite Groups And Related Topics
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Author : Irving Reiner
language : en
Publisher: American Mathematical Soc.
Release Date : 1971
Representation Theory Of Finite Groups And Related Topics written by Irving Reiner 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 1971 with Mathematics categories.
This symposium, on Representation Theory of Finite Groups and Related Topics, was held in conjunction with a sectional meeting of the American Mathematical Society, and in honor of professor Richard Brauer. Dr. Brauer's fundamental work in representation theory is at the heart of many further developments in the topic. These proceedings contain the articles of participants, based on their symposium presentations, and indicate the scope of current research in representation theory.
Lattices Over Orders Ii
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Author : Klaus W. Roggenkamp
language : en
Publisher: Springer
Release Date : 2006-11-15
Lattices Over Orders Ii written by Klaus W. Roggenkamp and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Groups Of Prime Power Order
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Author : Yakov G. Berkovich
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-12-14
Groups Of Prime Power Order written by Yakov G. Berkovich and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-14 with Mathematics categories.
This is the fourth volume of a comprehensive and elementary treatment of finite p-group theory. As in the previous volumes, minimal nonabelian p-groups play an important role. Topics covered in this volume include: subgroup structure of metacyclic p-groups Ishikawa’s theorem on p-groups with two sizes of conjugate classes p-central p-groups theorem of Kegel on nilpotence of H p-groups partitions of p-groups characterizations of Dedekindian groups norm of p-groups p-groups with 2-uniserial subgroups of small order The book also contains hundreds of original exercises and solutions and a comprehensive list of more than 500 open problems. This work is suitable for researchers and graduate students with a modest background in algebra.
A General Character Theory For Partially Ordered Sets And Lattices
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Author : Karl Heinrich Hofmann
language : en
Publisher: American Mathematical Soc.
Release Date : 1972
A General Character Theory For Partially Ordered Sets And Lattices written by Karl Heinrich Hofmann 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 1972 with Categories (Mathematics). categories.
Summaries Of Projects Completed In Fiscal Year
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Author :
language : en
Publisher:
Release Date :
Summaries Of Projects Completed In Fiscal Year written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Engineering categories.
Summaries Of Projects Completed
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Author : National Science Foundation (U.S.)
language : en
Publisher:
Release Date :
Summaries Of Projects Completed written by National Science Foundation (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Engineering categories.
Summaries Of Projects Completed In Fiscal Year
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Author : National Science Foundation (U.S.)
language : en
Publisher:
Release Date : 1979
Summaries Of Projects Completed In Fiscal Year written by National Science Foundation (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Engineering categories.