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Author : Kurt Augustus Hirsch
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.F/5 ( download)
Download or read book The Automorphism Groups of Abelian P-groups written by Kurt Augustus Hirsch and published by . This book was released on 1961 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M. Aschbacher
Publisher : Cambridge University Press
ISBN 13 : 9780521786751
Total Pages : 320 pages
Book Rating : 4.7/5 (867 download)
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.
Author : Yakov Berkovich
Publisher : Walter de Gruyter
ISBN 13 : 3110208237
Total Pages : 613 pages
Book Rating : 4.1/5 (12 download)
Download or read book Groups of Prime Power Order. Volume 2 written by Yakov Berkovich and published by Walter de Gruyter. This book was released on 2008-12-10 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of three volumes devoted to elementary finite p-group theory. Similar to the first volume, hundreds of important results are analyzed and, in many cases, simplified. Important topics presented in this monograph include: (a) classification of p-groups all of whose cyclic subgroups of composite orders are normal, (b) classification of 2-groups with exactly three involutions, (c) two proofs of Ward's theorem on quaternion-free groups, (d) 2-groups with small centralizers of an involution, (e) classification of 2-groups with exactly four cyclic subgroups of order 2n > 2, (f) two new proofs of Blackburn's theorem on minimal nonmetacyclic groups, (g) classification of p-groups all of whose subgroups of index p2 are abelian, (h) classification of 2-groups all of whose minimal nonabelian subgroups have order 8, (i) p-groups with cyclic subgroups of index p2 are classified. This volume contains hundreds of original exercises (with all difficult exercises being solved) and an extended list of about 700 open problems. The book is based on Volume 1, and it is suitable for researchers and graduate students of mathematics with a modest background on algebra.
Author : László Fuchs
Publisher : Springer
ISBN 13 : 3319194224
Total Pages : 762 pages
Book Rating : 4.3/5 (191 download)
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.
Author : Irving Kaplansky
Publisher :
ISBN 13 :
Total Pages : 91 pages
Book Rating : 4.:/5 (239 download)
Download or read book Infinite Abelian Groups written by Irving Kaplansky and published by . This book was released on 1954 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paulo Ney de Souza
Publisher : Springer Science & Business Media
ISBN 13 : 9780387204291
Total Pages : 614 pages
Book Rating : 4.2/5 (42 download)
Download or read book Berkeley Problems in Mathematics written by Paulo Ney de Souza and published by Springer Science & Business Media. This book was released on 2004-01-08 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.
Author : I. Martin Isaacs
Publisher : American Mathematical Society
ISBN 13 : 1470471604
Total Pages : 368 pages
Book Rating : 4.4/5 (74 download)
Download or read book Finite Group Theory written by I. Martin Isaacs and published by American Mathematical Society. This book was released on 2023-01-24 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur–Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem. Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a group-theoretic proof of Burnside's theorem about groups with order divisible by just two primes, the Wielandt automorphism tower theorem, Yoshida's transfer theorem, the “principal ideal theorem” of transfer theory and many smaller results that are not very well known. Proofs often contain original ideas, and they are given in complete detail. In many cases they are simpler than can be found elsewhere. The book is largely based on the author's lectures, and consequently, the style is friendly and somewhat informal. Finally, the book includes a large collection of problems at disparate levels of difficulty. These should enable students to practice group theory and not just read about it. Martin Isaacs is professor of mathematics at the University of Wisconsin, Madison. Over the years, he has received many teaching awards and is well known for his inspiring teaching and lecturing. He received the University of Wisconsin Distinguished Teaching Award in 1985, the Benjamin Smith Reynolds Teaching Award in 1989, and the Wisconsin Section MAA Teaching Award in 1993, to name only a few. He was also honored by being the selected MAA Pólya Lecturer in 2003–2005.
Author : Andrei V. Kelarev
Publisher : American Mathematical Soc.
ISBN 13 : 0821827510
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)
Download or read book Abelian Groups, Rings and Modules written by Andrei V. Kelarev and published by American Mathematical Soc.. This book was released on 2001 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings from the conference on Abelian Groups, Rings, and Modules (AGRAM) held at the University of Western Australia (Perth). Included are articles based on talks given at the conference, as well as a few specially invited papers. The proceedings were dedicated to Professor László Fuchs. The book includes a tribute and a review of his work by his long-time collaborator, Professor Luigi Salce. Four surveys from leading experts follow Professor Salce's article. They present recent results from active research areas
Author : Yakov Berkovich
Publisher : Walter de Gruyter
ISBN 13 : 3110208229
Total Pages : 533 pages
Book Rating : 4.1/5 (12 download)
Download or read book Groups of Prime Power Order. Volume 1 written by Yakov Berkovich and published by Walter de Gruyter. This book was released on 2008-12-10 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of three volumes of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this monograph include: (a) counting of subgroups, with almost all main counting theorems being proved, (b) regular p-groups and regularity criteria, (c) p-groups of maximal class and their numerous characterizations, (d) characters of p-groups, (e) p-groups with large Schur multiplier and commutator subgroups, (f) (p‒1)-admissible Hall chains in normal subgroups, (g) powerful p-groups, (h) automorphisms of p-groups, (i) p-groups all of whose nonnormal subgroups are cyclic, (j) Alperin's problem on abelian subgroups of small index. The book is suitable for researchers and graduate students of mathematics with a modest background on algebra. It also contains hundreds of original exercises (with difficult exercises being solved) and a comprehensive list of about 700 open problems.
Author : Evgenii I. Khukhro
Publisher : Cambridge University Press
ISBN 13 : 052159717X
Total Pages : 226 pages
Book Rating : 4.5/5 (215 download)
Download or read book P-Automorphisms of Finite P-Groups written by Evgenii I. Khukhro and published by Cambridge University Press. This book was released on 1998-02-13 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers working in group theory and Lie rings.
Author : Volodymyr Nekrashevych
Publisher : American Mathematical Soc.
ISBN 13 : 0821838318
Total Pages : 248 pages
Book Rating : 4.8/5 (218 download)
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.
Author : Dikran Dikranjan
Publisher : CRC Press
ISBN 13 : 1482276054
Total Pages : 468 pages
Book Rating : 4.4/5 (822 download)
Download or read book Abelian Groups, Module Theory, and Topology written by Dikran Dikranjan and published by CRC Press. This book was released on 2019-05-16 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.
Author : Marshall Hall Jr.
Publisher :
ISBN 13 : 9781258410780
Total Pages : 444 pages
Book Rating : 4.4/5 (17 download)
Download or read book The Theory of Groups written by Marshall Hall Jr. and published by . This book was released on 2012-06-01 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : William C. Arlinghaus
Publisher : American Mathematical Soc.
ISBN 13 : 0821823310
Total Pages : 98 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Classification of Minimal Graphs with Given Abelian Automorphism Group written by William C. Arlinghaus and published by American Mathematical Soc.. This book was released on 1985 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any finite abstract group can be realized as the automorphism group of a graph. The purpose of this memoir is to find the realization, for each finite abelian group, with the least number of vertices possible. The results are extended to all finite abelian groups. Thus a complete classification is provided for minimal graphs with given finite abelian automorphism group.
Author : W. Barth
Publisher : Springer
ISBN 13 : 3642577393
Total Pages : 439 pages
Book Rating : 4.6/5 (425 download)
Download or read book Compact Complex Surfaces written by W. Barth and published by Springer. This book was released on 2015-05-22 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants. Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces. Other developments include the systematic use of nef-divisors (in ac cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kahler structures on surfaces, and Reider's new approach to adjoint mappings. All these developments have been incorporated in the present edition, though the Donaldson and Seiberg-Witten theory only by way of examples. Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom we are much obliged.
Author : J. D. Dixon
Publisher : Cambridge University Press
ISBN 13 : 9780521542180
Total Pages : 392 pages
Book Rating : 4.5/5 (421 download)
Download or read book Analytic Pro-P Groups written by J. D. Dixon and published by Cambridge University Press. This book was released on 2003-09-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date treatment of analytic pro-p groups for graduate students and researchers.
Author : Bertram Wehrfritz
Publisher : Springer Science & Business Media
ISBN 13 : 3642870813
Total Pages : 243 pages
Book Rating : 4.6/5 (428 download)
Download or read book Infinite Linear Groups written by Bertram Wehrfritz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a linear group we mean essentially a group of invertible matrices with entries in some commutative field. A phenomenon of the last twenty years or so has been the increasing use of properties of infinite linear groups in the theory of (abstract) groups, although the story of infinite linear groups as such goes back to the early years of this century with the work of Burnside and Schur particularly. Infinite linear groups arise in group theory in a number of contexts. One of the most common is via the automorphism groups of certain types of abelian groups, such as free abelian groups of finite rank, torsion-free abelian groups of finite rank and divisible abelian p-groups of finite rank. Following pioneering work of Mal'cev many authors have studied soluble groups satisfying various rank restrictions and their automor phism groups in this way, and properties of infinite linear groups now play the central role in the theory of these groups. It has recently been realized that the automorphism groups of certain finitely generated soluble (in particular finitely generated metabelian) groups contain significant factors isomorphic to groups of automorphisms of finitely generated modules over certain commutative Noetherian rings. The results of our Chapter 13, which studies such groups of automorphisms, can be used to give much information here.
