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Soluble And Nilpotent Linear Groups
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Book Synopsis Soluble and Nilpotent Linear Groups by : Dmitriĭ Alekseevich Suprunenko
Download or read book Soluble and Nilpotent Linear Groups written by Dmitriĭ Alekseevich Suprunenko and published by American Mathematical Soc.. This book was released on 1963 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Soluble and Nilpotent Linear Groups by : D. A. Suprunenko
Download or read book Soluble and Nilpotent Linear Groups written by D. A. Suprunenko and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Soluble and Nilpotent Linear Groups by : Dmitrij A. Suprunenko
Download or read book Soluble and Nilpotent Linear Groups written by Dmitrij A. Suprunenko and published by . This book was released on 1970 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Infinite Linear Groups by : Bertram Wehrfritz
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.
Book Synopsis Soluble and nilpotent linear groups by : Dmitrij Alekseevi1c Suprunenko
Download or read book Soluble and nilpotent linear groups written by Dmitrij Alekseevi1c Suprunenko and published by . This book was released on 1963 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nilpotent Groups and their Automorphisms by : Evgenii I. Khukhro
Download or read book Nilpotent Groups and their Automorphisms written by Evgenii I. Khukhro and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Infinite Soluble and Nilpotent Groups by : Derek John Scott Robinson
Download or read book Infinite Soluble and Nilpotent Groups written by Derek John Scott Robinson and published by . This book was released on 1968 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Theory of Infinite Soluble Groups by : John C. Lennox
Download or read book The Theory of Infinite Soluble Groups written by John C. Lennox and published by Clarendon Press. This book was released on 2004-08-19 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central concept in this monograph is that of a soluble group - a group which is built up from abelian groups by repeatedly forming group extensions. It covers all the major areas, including finitely generated soluble groups, soluble groups of finite rank, modules over group rings, algorithmic problems, applications of cohomology, and finitely presented groups, whilst remaining fairly strictly within the boundaries of soluble group theory. An up-to-date survey of the area aimed at research students and academic algebraists and group theorists, it is a compendium of information that will be especially useful as a reference work for researchers in the field.
Book Synopsis Finiteness Conditions and Generalized Soluble Groups by : Derek J.S. Robinson
Download or read book Finiteness Conditions and Generalized Soluble Groups written by Derek J.S. Robinson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of group theoretical properties of two disparate kinds, firstly finiteness conditions or generalizations of finiteness and secondly generalizations of solubility or nilpotence. It will be particularly interesting to discuss groups which possess properties of both types. The origins of the subject may be traced back to the nineteen twenties and thirties and are associated with the names of R. Baer, S.N. Cernikov, K.A. Hirsch, A.G. Kuros, 0.]. Schmidt and H. Wielandt. Since this early period, the body of theory has expanded at an increasingly rapid rate through the efforts of many group theorists, particularly in Germany, Great Britain and the Soviet Union. Some of the highest points attained can, perhaps, be found in the work of P. Hall and A.I. Mal'cev on infinite soluble groups. Kuras's well-known book "The theory of groups" has exercised a strong influence on the development of the theory of infinite groups: this is particularly true of the second edition in its English translation of 1955. To cope with the enormous increase in knowledge since that date, a third volume, containing a survey of the contents of a very large number of papers but without proofs, was added to the book in 1967
Book Synopsis Matrix Groups by : Dmitriĭ Alekseevich Suprunenko
Download or read book Matrix Groups written by Dmitriĭ Alekseevich Suprunenko and published by American Mathematical Soc.. This book was released on 1976 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a translation from the Russian of D.A. Suprunenko's book which was published in the Soviet Union in 1972. The translation was edited by K.A. Hirsch. The book gives an account of the classical results on the structure of normal subgroups of the general linear group over a division ring, of Burnside's and Schur's theorems on periodic linear groups, and of the theorem on the normal structure of SL(n, Z) for n >2. The theory of solvable, nilpotent, and locally nilpotent linear groups is also discussed.
Download or read book Linear Groups written by Martyn R. Dixon and published by CRC Press. This book was released on 2020-04-03 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional linear groups. The theory of finite dimensional linear groups is one of the best developed algebraic theories. The array of articles devoted to this topic is enormous, and there are many monographs concerned with matrix groups, ranging from old, classical texts to ones published more recently. However, in the case when the dimension is infinite (and such cases arise quite often), the reality is quite different. The situation with the study of infinite dimensional linear groups is like the situation that has developed in the theory of groups, in the transition from the study of finite groups to the study of infinite groups which appeared about one hundred years ago. It is well known that this transition was extremely efficient and led to the development of a rich and central branch of algebra: Infinite group theory. The hope is that this book can be part of a similar transition in the field of linear groups. Features This is the first book dedicated to infinite-dimensional linear groups This is written for experts and graduate students specializing in algebra and parallel disciplines This book discusses a very new theory and accumulates many important and useful results
Download or read book Algebra IV written by A.I. Kostrikin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group theory is one of the most fundamental branches of mathematics. This highly accessible volume of the Encyclopaedia is devoted to two important subjects within this theory. Extremely useful to all mathematicians, physicists and other scientists, including graduate students who use group theory in their work.
Book Synopsis Model Theory of Groups and Automorphism Groups by : David M. Evans
Download or read book Model Theory of Groups and Automorphism Groups written by David M. Evans and published by Cambridge University Press. This book was released on 1997-07-10 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys recent interactions between model theory and other branches of mathematics, notably group theory.
Book Synopsis Soluble and Nilpotent Linear Groups by : D. Suprunenko
Download or read book Soluble and Nilpotent Linear Groups written by D. Suprunenko and published by . This book was released on 1963 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solvable and Nilpotent Groups by : A. G. Kuroš
Download or read book Solvable and Nilpotent Groups written by A. G. Kuroš and published by . This book was released on 1953 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Course in the Theory of Groups by : Derek J.S. Robinson
Download or read book A Course in the Theory of Groups written by Derek J.S. Robinson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: " A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a one-line explanation as any. The concept of a group is surely one of the central ideas of mathematics. Certainly there are a few branches of that science in which groups are not employed implicitly or explicitly. Nor is the use of groups confined to pure mathematics. Quantum theory, molecular and atomic structure, and crystallography are just a few of the areas of science in which the idea of a group as a measure of symmetry has played an important part. The theory of groups is the oldest branch of modern algebra. Its origins are to be found in the work of Joseph Louis Lagrange (1736-1813), Paulo Ruffini (1765-1822), and Evariste Galois (1811-1832) on the theory of algebraic equations. Their groups consisted of permutations of the variables or of the roots of polynomials, and indeed for much of the nineteenth century all groups were finite permutation groups. Nevertheless many of the fundamental ideas of group theory were introduced by these early workers and their successors, Augustin Louis Cauchy (1789-1857), Ludwig Sylow (1832-1918), Camille Jordan (1838-1922) among others. The concept of an abstract group is clearly recognizable in the work of Arthur Cayley (1821-1895) but it did not really win widespread acceptance until Walther von Dyck (1856-1934) introduced presentations of groups.
Book Synopsis Group and Ring Theoretic Properties of Polycyclic Groups by : B.A.F. Wehrfritz
Download or read book Group and Ring Theoretic Properties of Polycyclic Groups written by B.A.F. Wehrfritz and published by Springer Science & Business Media. This book was released on 2009-11-28 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations. The book is intended to be a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch. Thus it has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. An extensive bibliography then concludes the book.
