The Theory Of Infinite Soluble Groups
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Author | : John C. Lennox |
Publisher | : Clarendon Press |
Total Pages | : 360 |
Release | : 2004-08-19 |
Genre | : Mathematics |
ISBN | : 0191523151 |
Download The Theory of Infinite Soluble Groups Book in PDF, Epub and Kindle
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.
Author | : John Carson Lennox |
Publisher | : |
Total Pages | : 342 |
Release | : 2004 |
Genre | : Infinite groups |
ISBN | : 9780191709326 |
Download The Theory of Infinite Soluble Groups Book in PDF, Epub and Kindle
The central concept of this book is that of a soluble group: a group that is built up from abelian groups by repeatedly forming group extensions. It covers finitely generated soluble groups soluble groups of finite rank, modules over group rings, & much else within the boundaries of soluble group theory.
Author | : Derek J.S. Robinson |
Publisher | : Springer Science & Business Media |
Total Pages | : 226 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662072416 |
Download Finiteness Conditions and Generalized Soluble Groups Book in PDF, Epub and Kindle
This book is a study of group theoretical properties of two dis parate kinds, firstly finiteness conditions or generalizations of fini teness 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. Wie landt. 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.
Author | : A.I. Kostrikin |
Publisher | : Springer Science & Business Media |
Total Pages | : 210 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3662028697 |
Download Algebra IV Book in PDF, Epub and Kindle
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.
Author | : Bertram Wehrfritz |
Publisher | : Springer Science & Business Media |
Total Pages | : 243 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642870813 |
Download Infinite Linear Groups Book in PDF, Epub and Kindle
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.
Author | : Derek J.S. Robinson |
Publisher | : Springer Science & Business Media |
Total Pages | : 498 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468401289 |
Download A Course in the Theory of Groups Book in PDF, Epub and Kindle
" 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.
Author | : Paul Baginski |
Publisher | : World Scientific |
Total Pages | : 258 |
Release | : 2017-12-26 |
Genre | : Mathematics |
ISBN | : 9813204060 |
Download Infinite Group Theory: From The Past To The Future Book in PDF, Epub and Kindle
The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest.
Author | : Olaf Manz |
Publisher | : Cambridge University Press |
Total Pages | : 318 |
Release | : 1993-09-16 |
Genre | : Mathematics |
ISBN | : 0521397391 |
Download Representations of Solvable Groups Book in PDF, Epub and Kindle
Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtained can then be applied to infinite modules, and in particular to character theory (ordinary and Brauer) of solvable groups. The authors include proofs of Brauer's height zero conjecture and the Alperin-McKay conjecture for solvable groups. Gluck's permutation lemma and Huppert's classification of solvable two-transive permutation groups, which are essentially results about finite modules of finite groups, play important roles in the applications and a new proof is given of the latter. Researchers into group theory, representation theory, or both, will find that this book has much to offer.
Author | : Elizabeth Wharton |
Publisher | : |
Total Pages | : 336 |
Release | : 2006 |
Genre | : Group theory |
ISBN | : |
Download The Model Theory of Certain Infinite Soluble Groups Book in PDF, Epub and Kindle
Author | : John S. Rose |
Publisher | : Courier Corporation |
Total Pages | : 322 |
Release | : 2013-05-27 |
Genre | : Mathematics |
ISBN | : 0486170667 |
Download A Course on Group Theory Book in PDF, Epub and Kindle
Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as applications. 679 exercises. 1978 edition.