Download or read book Ordered Groups and Infinite Permutation Groups written by W.C. Holland and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Notes on Infinite Permutation Groups written by Meenaxi Bhattacharjee and published by Springer Science & Business Media. This book was released on 1998-11-20 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ordered Permutation Groups written by Andrew Martin William Glass and published by Cambridge University Press. This book was released on 1981 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Notes on Infinite Permutation Groups written by M Bhattacharjee and published by Springer. This book was released on 1997-01-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Permutation Groups written by John D. Dixon and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Right Ordered Groups written by Valeriĭ Matveevich Kopytov and published by Springer Science & Business Media. This book was released on 1996-04-30 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Permutation Groups written by Peter J. Cameron and published by Cambridge University Press. This book was released on 1999-02-04 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes recent developments in the study of permutation groups for beginning graduate students.
Download or read book Groups written by Antonio Machì and published by Springer Science & Business Media. This book was released on 2012-04-05 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder’s program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.
Download or read book Representations of the Infinite Symmetric Group written by Alexei Borodin and published by Cambridge University Press. This book was released on 2017 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
Download or read book Enumeration of Orbits of Infinite Permutation Groups written by Dugald Macpherson and published by . This book was released on 1983 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Oligomorphic Permutation Groups written by Peter J. Cameron and published by Cambridge University Press. This book was released on 1990-06-29 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Permutation Groups written by Donald S. Passman and published by . This book was released on 1968 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Permutation Groups written by Helmut Wielandt and published by Academic Press. This book was released on 2014-05-10 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups. Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius' theory of group characters. This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.
Download or read book Partially Ordered Groups written by Andrew Martin William Glass and published by World Scientific. This book was released on 1999 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Download or read book Infinite Group Theory From The Past To The Future written by Paul Baginski and published by World Scientific. This book was released on 2017-12-26 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite and Infinite Combinatorics in Sets and Logic written by Norbert W Sauer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the accounts of papers delivered at the Nato Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic held at the Banff Centre, Alberta, Canada from April 21 to May 4, 1991. As the title suggests the meeting brought together workers interested in the interplay between finite and infinite combinatorics, set theory, graph theory and logic. It used to be that infinite set theory, finite combinatorics and logic could be viewed as quite separate and independent subjects. But more and more those disciplines grow together and become interdependent of each other with ever more problems and results appearing which concern all of those disciplines. I appreciate the financial support which was provided by the N. A. T. O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the Department of Mathematics and Statistics of the University of Calgary. 11l'te meeting on Finite and Infinite Combinatorics in Sets and Logic followed two other meetings on discrete mathematics held in Banff, the Symposium on Ordered Sets in 1981 and the Symposium on Graphs and Order in 1984. The growing inter-relation between the different areas in discrete mathematics is maybe best illustrated by the fact that many of the participants who were present at the previous meetings also attended this meeting on Finite and Infinite Combinatorics in Sets and Logic.
Download or read book Notes on Infinite Permutation Groups written by Meenaxi Bhattacharjee and published by . This book was released on 2014-01-15 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
