The Direct Product Of A Finite Number Of Finite Groups

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Products of Finite Groups

Author : Adolfo Ballester-Bolinches
Publisher : Walter de Gruyter
ISBN 13 : 311022061X
Total Pages : 347 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Products of Finite Groups by : Adolfo Ballester-Bolinches

Download or read book Products of Finite Groups written by Adolfo Ballester-Bolinches and published by Walter de Gruyter. This book was released on 2010-10-19 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of finite groups factorised as a product of two or more subgroups has become a subject of great interest during the last years with applications not only in group theory, but also in other areas like cryptography and coding theory. It has experienced a big impulse with the introduction of some permutability conditions. The aim of this book is to gather, order, and examine part of this material, including the latest advances made, give some new approach to some topics, and present some new subjects of research in the theory of finite factorised groups. Some of the topics covered by this book include groups whose subnormal subgroups are normal, permutable, or Sylow-permutable, products of nilpotent groups, and an exhaustive structural study of totally and mutually permutable products of finite groups and their relation with classes of groups. This monograph is mainly addressed to graduate students and senior researchers interested in the study of products and permutability of finite groups. A background in finite group theory and a basic knowledge of representation theory and classes of groups is recommended to follow it.

Theory of Groups of Finite Order

Author : William S. Burnside
Publisher : Courier Corporation
ISBN 13 : 0486159442
Total Pages : 545 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Theory of Groups of Finite Order by : William S. Burnside

Download or read book Theory of Groups of Finite Order written by William S. Burnside and published by Courier Corporation. This book was released on 2013-02-20 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic 1911 edition covers many group-related properties, including an extensive treatment of permutation groups and groups of linear substitutions, along with graphic representation of groups, congruence groups, and special topics.

Abstract Algebra

Author : Thomas Judson
Publisher : Orthogonal Publishing L3c
ISBN 13 : 9781944325190
Total Pages : 0 pages
Book Rating : 4.3/5 (251 download)

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Book Synopsis Abstract Algebra by : Thomas Judson

Download or read book Abstract Algebra written by Thomas Judson and published by Orthogonal Publishing L3c. This book was released on 2023-08-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

A Course in Finite Group Representation Theory

Author : Peter Webb
Publisher : Cambridge University Press
ISBN 13 : 1107162394
Total Pages : 339 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis A Course in Finite Group Representation Theory by : Peter Webb

Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

The Finite Simple Groups

Author : Robert Wilson
Publisher : Springer Science & Business Media
ISBN 13 : 1848009879
Total Pages : 310 pages
Book Rating : 4.8/5 (48 download)

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Book Synopsis The Finite Simple Groups by : Robert Wilson

Download or read book The Finite Simple Groups written by Robert Wilson and published by Springer Science & Business Media. This book was released on 2009-12-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thisbookisintendedasanintroductiontoallthe?nitesimplegroups.During themonumentalstruggletoclassifythe?nitesimplegroups(andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi?cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian) ?nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per- tation groups, which is well served by the classic text of Wielandt [170]and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].

Representations of Finite Groups

Author : Hirosi Nagao
Publisher : Elsevier
ISBN 13 : 1483269930
Total Pages : 443 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Representations of Finite Groups by : Hirosi Nagao

Download or read book Representations of Finite Groups written by Hirosi Nagao and published by Elsevier. This book was released on 2014-05-10 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representations of Finite Groups provides an account of the fundamentals of ordinary and modular representations. This book discusses the fundamental theory of complex representations of finite groups. Organized into five chapters, this book begins with an overview of the basic facts about rings and modules. This text then provides the theory of algebras, including theories of simple algebras, Frobenius algebras, crossed products, and Schur indices with representation-theoretic versions of them. Other chapters include a survey of the fundamental theory of modular representations, with emphasis on Brauer characters. This book discusses as well the module-theoretic representation theory due to Green and includes some topics such as Burry–Carlson's theorem and Scott modules. The final chapter deals with the fundamental results of Brauer on blocks and Fong's theory of covering, and includes some approaches to them. This book is a valuable resource for readers who are interested in the various approaches to the study of the representations of groups.

Finite Simple Groups

Author : Daniel Gorenstein
Publisher : Springer Science & Business Media
ISBN 13 : 1468484974
Total Pages : 339 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Finite Simple Groups by : Daniel Gorenstein

Download or read book Finite Simple Groups written by Daniel Gorenstein and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: In February 1981, the classification of the finite simple groups (Dl)* was completed,t. * representing one of the most remarkable achievements in the history or mathematics. Involving the combined efforts of several hundred mathematicians from around the world over a period of 30 years, the full proof covered something between 5,000 and 10,000 journal pages, spread over 300 to 500 individual papers. The single result that, more than any other, opened up the field and foreshadowed the vastness of the full classification proof was the celebrated theorem of Walter Feit and John Thompson in 1962, which stated that every finite group of odd order (D2) is solvable (D3)-a statement expressi ble in a single line, yet its proof required a full 255-page issue of the Pacific 10urnal of Mathematics [93]. Soon thereafter, in 1965, came the first new sporadic simple group in over 100 years, the Zvonimir Janko group 1 , to further stimulate the 1 'To make the book as self-contained as possible. we are including definitions of various terms as they occur in the text. However. in order not to disrupt the continuity of the discussion. we have placed them at the end of the Introduction. We denote these definitions by (DI). (D2), (D3). etc.

Representation Theory of Finite Groups

Author : Benjamin Steinberg
Publisher : Springer Science & Business Media
ISBN 13 : 1461407761
Total Pages : 166 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Representation Theory of Finite Groups by : Benjamin Steinberg

Download or read book Representation Theory of Finite Groups written by Benjamin Steinberg and published by Springer Science & Business Media. This book was released on 2011-10-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

Cellular Automata and Groups

Author : Tullio Ceccherini-Silberstein
Publisher : Springer Science & Business Media
ISBN 13 : 3642140343
Total Pages : 446 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Cellular Automata and Groups by : Tullio Ceccherini-Silberstein

Download or read book Cellular Automata and Groups written by Tullio Ceccherini-Silberstein and published by Springer Science & Business Media. This book was released on 2010-08-24 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.

Applications of Finite Groups

Author : J. S. Lomont
Publisher : Academic Press
ISBN 13 : 1483268969
Total Pages : 359 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Applications of Finite Groups by : J. S. Lomont

Download or read book Applications of Finite Groups written by J. S. Lomont and published by Academic Press. This book was released on 2014-05-12 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.

Self-Similar Groups

Author : Volodymyr Nekrashevych
Publisher : American Mathematical Soc.
ISBN 13 : 0821838318
Total Pages : 248 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Self-Similar Groups by : Volodymyr Nekrashevych

Download or read book Self-Similar Groups written by Volodymyr Nekrashevych and published by American Mathematical Soc.. This book was released on 2005 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. This connection is established through the central topics of the book, which are the notions of the iterated monodromy group and limit space. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. In particular, it is shown that Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties can appear not just as isolated examples, but as naturally defined iterated monodromy groups of rational functions. The book offers important, new mathematics that will open new avenues of research in group theory and dynamical systems. It is intended to be accessible to a wide readership of professional mathematicians.

Finite Group Theory

Author : M. Aschbacher
Publisher : Cambridge University Press
ISBN 13 : 9780521786751
Total Pages : 320 pages
Book Rating : 4.7/5 (867 download)

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Book Synopsis Finite Group Theory by : M. Aschbacher

Download or read book Finite Group Theory written by M. Aschbacher and published by Cambridge University Press. This book was released on 2000-06-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 40 years the theory of finite groups has developed dramatically. The finite simple groups have been classified and are becoming better understood. Tools exist to reduce many questions about arbitrary finite groups to similar questions about simple groups. Since the classification there have been numerous applications of this theory in other branches of mathematics. Finite Group Theory develops the foundations of the theory of finite groups. It can serve as a text for a course on finite groups for students already exposed to a first course in algebra. It could supply the background necessary to begin reading journal articles in the field. For specialists it also provides a reference on the foundations of the subject. This second edition has been considerably improved with a completely rewritten Chapter 15 considering the 2-Signalizer Functor Theorem, and the addition of an appendix containing solutions to exercises.

Group Theory

Author : R. Mirman
Publisher : World Scientific
ISBN 13 : 9789810233655
Total Pages : 494 pages
Book Rating : 4.2/5 (336 download)

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Book Synopsis Group Theory by : R. Mirman

Download or read book Group Theory written by R. Mirman and published by World Scientific. This book was released on 1995 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough introduction to group theory, this (highly problem-oriented) book goes deeply into the subject to provide a fuller understanding than available anywhere else. The book aims at, not only teaching the material, but also helping to develop the skills needed by a researcher and teacher, possession of which will be highly advantageous in these very competitive times, particularly for those at the early, insecure, stages of their careers. And it is organized and written to serve as a reference to provide a quick introduction giving the essence and vocabulary useful for those who need only some slight knowledge, those just learning, as well as researchers, and especially for the latter it provides a grasp, and often material and perspective, not otherwise available.

Cohomology of Finite Groups

Author : Alejandro Adem
Publisher : Springer Science & Business Media
ISBN 13 : 3662062828
Total Pages : 333 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Cohomology of Finite Groups by : Alejandro Adem

Download or read book Cohomology of Finite Groups written by Alejandro Adem and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important new fields in mathematics, like homological algebra and algebraic K-theory. This is the first book to deal comprehensively with the cohomology of finite groups: it introduces the most important and useful algebraic and topological techniques, and describes the interplay of the subject with those of homotopy theory, representation theory and group actions. The combination of theory and examples, together with the techniques for computing the cohomology of important classes of groups including symmetric groups, alternating groups, finite groups of Lie type, and some of the sporadic simple groups, enable readers to acquire an in-depth understanding of group cohomology and its extensive applications.

Theory and Applications of Finite Groups

Author : George Abram Miller
Publisher :
ISBN 13 :
Total Pages : 413 pages
Book Rating : 4.L/5 ( download)

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Book Synopsis Theory and Applications of Finite Groups by : George Abram Miller

Download or read book Theory and Applications of Finite Groups written by George Abram Miller and published by . This book was released on 1916 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry of Defining Relations in Groups

Author : A.Yu. Ol'shanskii
Publisher : Springer Science & Business Media
ISBN 13 : 9401136181
Total Pages : 530 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Geometry of Defining Relations in Groups by : A.Yu. Ol'shanskii

Download or read book Geometry of Defining Relations in Groups written by A.Yu. Ol'shanskii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Ht moi - ..., si favait su comment en reveniT, One service mathematics hal rendered the je n'y serais point aile.' human race. It has put C.

Abelian Groups

Author : László Fuchs
Publisher : Springer
ISBN 13 : 3319194224
Total Pages : 762 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Abelian Groups by : László Fuchs

Download or read book Abelian Groups written by László Fuchs and published by Springer. This book was released on 2015-12-12 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of un decidability problems. The treatment of the latter trend includes Shelah’s seminal work on the un decidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology and homological algebra. An abundance of exercises are included to test the reader’s comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject’s further development.