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Complementation Of Normal Subgroups

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Complementation Of Normal Subgroups

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Author : Joseph Kirtland
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-09-11

Complementation Of Normal Subgroups written by Joseph Kirtland 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 2017-09-11 with Mathematics categories.

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

Subgroup Lattices Of Groups

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Author : Roland Schmidt
language : en
Publisher: Walter de Gruyter
Release Date : 2011-07-20

Subgroup Lattices Of Groups written by Roland Schmidt and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-20 with Mathematics categories.

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Classes Of Finite Groups

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Author : Adolfo Ballester-Bolinches
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-10

Classes Of Finite Groups written by Adolfo Ballester-Bolinches 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 2006-07-10 with Mathematics categories.

Many group theorists all over the world have been trying in the last twenty-five years to extend and adapt the magnificent methods of the Theory of Finite Soluble Groups to the more ambitious universe of all finite groups. This is a natural progression after the classification of finite simple groups but the achievements in this area are scattered in various papers. Our objectives in this book were to gather, order and examine all this material, including the latest advances made, give a new approach to some classic topics, shed light on some fundamental facts that still remain unpublished and present some new subjects of research in the theory of classes of finite, not necessarily solvable, groups.

Profinite Groups

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Author : Luis Ribes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09

Profinite Groups written by Luis Ribes 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 2013-04-09 with Mathematics categories.

The aim of this book is to serve both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. In neither of these two aspects have we tried to be encyclopedic. After some necessary background, we thoroughly develop the basic properties of profinite groups and introduce the main tools of the subject in algebra, topology and homol ogy. Later we concentrate on some topics that we present in detail, including recent developments in those areas. Interest in profinite groups arose first in the study of the Galois groups of infinite Galois extensions of fields. Indeed, profinite groups are precisely Galois groups and many of the applications of profinite groups are related to number theory. Galois groups carry with them a natural topology, the Krull topology. Under this topology they are Hausdorff compact and totally dis connected topological groups; these properties characterize profinite groups. Another important fact about profinite groups is that they are determined by their finite images under continuous homomorphisms: a profinite group is the inverse limit of its finite images. This explains the connection with abstract groups. If G is an infinite abstract group, one is interested in deducing prop erties of G from corresponding properties of its finite homomorphic images.

Structure Of A Group And The Structure Of Its Lattice Of Subgroups

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Author : Michio Suzuki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Structure Of A Group And The Structure Of Its Lattice Of Subgroups written by Michio Suzuki 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 2012-12-06 with Mathematics categories.

The central theme of this monograph is the relation between the structure of a group and the structure of its lattice of subgroups. Since the first papers on this topic have appeared, notably those of BAER and ORE, a large body of literature has grown up around this theory, and it is our aim to give a picture of the present state of this theory. To obtain a systematic treatment of the subject quite a few unpublished results of the author had to be included. On the other hand, it is natural that we could not reproduce every detail and had to treat some parts some wh at sketchily. We have tried to make this report as self-contained as possible. Accordingly we have given some proofs in considerable detail, though of course it is in the nature of such areport that many proofs have to be omitted or can only be given in outline. Similarly references to the concepts and theorems used are almost exclusively references to standard works like BIRKHOFF [lJ and ZASSENHAUS [lJ. The author would like to express his sincere gratitude to Professors REINHOLD BAER and DONALD G. HIGMAN for their kindness in giving hirn many valuable suggestions. His thanks are also due to Dr. NOBORU ITo who, during stimulating conversations, contributed many useful ideas. Urbana, May, 1956. M. Suzuki. Contents.

Finite Soluble Groups

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Author : Klaus Doerk
language : en
Publisher: Walter de Gruyter
Release Date : 2011-04-20

Finite Soluble Groups written by Klaus Doerk and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-20 with Mathematics categories.

Algebra

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Author : I. Martin Isaacs
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Algebra written by I. Martin Isaacs 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 2009 with Mathematics categories.

as a student." --Book Jacket.

The Theory Of Classes Of Groups

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Author : Guo Wenbin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Theory Of Classes Of Groups written by Guo Wenbin 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 2012-12-06 with Mathematics categories.

One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of alge bras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. ln his re ports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Con ference and to another international mathematics congress, striking the ories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F.

An Introduction To The Theory Of Groups

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Author : Joseph J. Rotman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

An Introduction To The Theory Of Groups written by Joseph J. Rotman 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 2012-12-06 with Mathematics categories.

Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions. From the reviews: "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route." --MATHEMATICAL REVIEWS

The Theory Of Groups

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Author : Hans J. Zassenhaus
language : en
Publisher: Courier Corporation
Release Date : 2013-09-16

The Theory Of Groups written by Hans J. Zassenhaus and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-16 with Mathematics categories.

Well-written graduate-level text acquaints reader with group-theoretic methods and demonstrates their usefulness in mathematics. Axioms, the calculus of complexes, homomorphic mapping, p-group theory, more. Many proofs shorter and more transparent than older ones.

Complementation Of Normal Subgroups

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