Ordered Groups And Infinite Permutation Groups PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Ordered Groups And Infinite Permutation Groups PDF full book. Access full book title Ordered Groups And Infinite Permutation Groups.
| Author | : W.C. Holland |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 252 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461334438 |
Download Ordered Groups and Infinite Permutation Groups Book in PDF, ePub and Kindle
The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that time, both P. Conrad and P. Cohn had showed that a group admits a total right ordering if and only if the group is a group of automor phisms of a totally ordered set. (In a right ordered group, the order is required to be preserved by all right translations, unlike a (two-sided) ordered group, where both right and left translations must preserve the order.
| Author | : Meenaxi Bhattacharjee |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 224 |
| Release | : 1998-11-20 |
| Genre | : Mathematics |
| ISBN | : 9783540649656 |
Download Notes on Infinite Permutation Groups Book in PDF, ePub and Kindle
The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions. There is basic background in both group theory and the necessary model theory, and the following topics are covered: transitivity and primitivity; symmetric groups and general linear groups; wreatch products; automorphism groups of various treelike objects; model-theoretic constructions for building structures with rich automorphism groups, the structure and classification of infinite primitive Jordan groups (surveyed); applications and open problems. With many examples and exercises, the book is intended primarily for a beginning graduate student in group theory.
| Author | : Andrew Martin William Glass |
| Publisher | : Cambridge University Press |
| Total Pages | : 333 |
| Release | : 1981 |
| Genre | : Mathematics |
| ISBN | : 0521241901 |
Download Ordered Permutation Groups Book in PDF, ePub and Kindle
As a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered, there is a natural subgroup to study, namely the set of permutations that preserves that order. In some senses. these are universal for automorphisms of models of theories. The purpose of this book is to make a thorough, comprehensive examination of these groups of permutations. After providing the initial background Professor Glass develops the general structure theory, emphasizing throughout the geometric and intuitive aspects of the subject. He includes many applications to infinite simple groups, ordered permutation groups and lattice-ordered groups. The streamlined approach will enable the beginning graduate student to reach the frontiers of the subject smoothly and quickly. Indeed much of the material included has never been available in book form before, so this account should also be useful as a reference work for professionals.
| Author | : John D. Dixon |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 360 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461207312 |
Download Permutation Groups Book in PDF, ePub and Kindle
Following the basic ideas, standard constructions and important examples in the theory of permutation groups, the book goes on to develop the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal ONan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. With its many exercises and detailed references to the current literature, this text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, as well as for self-study.
| Author | : Valeriĭ Matveevich Kopytov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 268 |
| Release | : 1996-04-30 |
| Genre | : Mathematics |
| ISBN | : 9780306110603 |
Download Right-Ordered Groups Book in PDF, ePub and Kindle
The notion of right-ordered groups is fundamental in theories of I-groups, ordered groups, torsion-free groups, and the theory of zero-divisors free rings, as well as in theoretical physics. Right-Ordered Groups is the first book to provide a systematic presentation of right-ordered group theory, describing all known and new results in the field. The volume addresses topics such as right-ordered groups and order permutation groups, the system of convex subgroups of a right-ordered group, and free products of right-ordered groups.
| Author | : Peter J. Cameron |
| Publisher | : Cambridge University Press |
| Total Pages | : 236 |
| Release | : 1999-02-04 |
| Genre | : Mathematics |
| ISBN | : 9780521653787 |
Download Permutation Groups Book in PDF, ePub and Kindle
This book summarizes recent developments in the study of permutation groups for beginning graduate students.
| Author | : Alexei Borodin |
| Publisher | : Cambridge University Press |
| Total Pages | : 169 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 1107175550 |
Download Representations of the Infinite Symmetric Group Book in PDF, ePub and Kindle
An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
| Author | : Peter J. Cameron |
| Publisher | : Cambridge University Press |
| Total Pages | : 172 |
| Release | : 1990-06-29 |
| Genre | : Mathematics |
| ISBN | : 0521388368 |
Download Oligomorphic Permutation Groups Book in PDF, ePub and Kindle
The study of permutations groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. This book discusses such structures, their substructures and their automorphism groups using a wide range of techniques.
| Author | : A. M. W. Glass |
| Publisher | : |
| Total Pages | : 266 |
| Release | : 1981 |
| Genre | : Ordered groups |
| ISBN | : |
Download Ordered Permutation Groups Book in PDF, ePub and Kindle
| Author | : A M W Glass |
| Publisher | : World Scientific |
| Total Pages | : 324 |
| Release | : 1999-07-22 |
| Genre | : Mathematics |
| ISBN | : 981449609X |
Download Partially Ordered Groups Book in PDF, ePub and Kindle
Recently the theory of partially ordered groups has been used by analysts, algebraists, topologists and model theorists. This book presents the most important results and topics in the theory with proofs that rely on (and interplay with) other areas of mathematics. It concludes with a list of some unsolved problems for the reader to tackle. In stressing both the special techniques of the discipline and the overlap with other areas of pure mathematics, the book should be of interest to a wide audience in diverse areas of mathematics. Contents:Definitions and ExamplesBasic PropertiesValues, Primes and PolarsAbelian and Normal-Valued Lattice-Ordered GroupsArchimedean Function GroupsSoluble Right Partially Ordered Groups and GeneralisationsPermutationsApplicationsCompletionsVarieties of Lattice-Ordered GroupsUnsolved Problems Readership: Pure mathematicians. Keywords:Partially Ordered Group;Lattice Ordered Group;Abelian Lattice Ordered Group;Completion;VarietyReviews: “The author's style of writing is very lucid, and the material presented is self-contained. It is an excellent reference text for a graduate course in this area, as well as a source of material for individual reading.” Bulletin of London Mathematical Society “This monograph is clearly written, well organized … can be warmly recommended to students and research workers dealing with the theory of partially ordered groups.” Mathematics Abstracts “Glass's book will get the reader to the forefront of research in the field and would be a suitable text for students in modern algebra, group theory, or ordered structures. It will surely find its place in all mathematical libraries and on the desks of the professional algebraists and 'ordered-groupers'.” Mathematical Reviews
