Ordered Groups And Infinite Permutation Groups

Author : W.C. Holland
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 46,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334439

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Ordered Groups and Infinite Permutation Groups by W.C. Holland Pdf

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,Dugald Macpherson,Rögnvaldur G. Möller,Peter M. Neumann
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 41,6 Mb
Release : 1998-11-20
Category : Mathematics
ISBN : 3540649654

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Notes on Infinite Permutation Groups by Meenaxi Bhattacharjee,Dugald Macpherson,Rögnvaldur G. Möller,Peter M. Neumann Pdf

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
Page : 333 pages
File Size : 45,5 Mb
Release : 1981
Category : Mathematics
ISBN : 9780521241908

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Ordered Permutation Groups by Andrew Martin William Glass Pdf

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 : Valeriĭ Matveevich Kopytov,V.M. Kopytov,Nikolai Yakovlevich Medvedev
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 40,7 Mb
Release : 1996-04-30
Category : Mathematics
ISBN : 0306110601

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Right-Ordered Groups by Valeriĭ Matveevich Kopytov,V.M. Kopytov,Nikolai Yakovlevich Medvedev Pdf

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 : John D. Dixon,Brian Mortimer
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207313

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Permutation Groups by John D. Dixon,Brian Mortimer Pdf

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 : Peter J. Cameron
Publisher : Cambridge University Press
Page : 236 pages
File Size : 53,9 Mb
Release : 1999-02-04
Category : Mathematics
ISBN : 0521653789

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Permutation Groups by Peter J. Cameron Pdf

This book summarizes recent developments in the study of permutation groups for beginning graduate students.

Author : Meenaxi Bhattacharjee,Rögnvaldur G. Möller,Dugald Macpherson,Peter M. Neumann
Publisher : Springer
Page : 206 pages
File Size : 47,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540498131

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Notes on Infinite Permutation Groups by Meenaxi Bhattacharjee,Rögnvaldur G. Möller,Dugald Macpherson,Peter M. Neumann Pdf

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 : A M W Glass
Publisher : World Scientific
Page : 324 pages
File Size : 46,8 Mb
Release : 1999-07-22
Category : Mathematics
ISBN : 9789814496094

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Partially Ordered Groups by A M W Glass Pdf

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

Author : Peter J. Cameron
Publisher : Cambridge University Press
Page : 172 pages
File Size : 53,5 Mb
Release : 1990-06-29
Category : Mathematics
ISBN : 9780521388368

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Oligomorphic Permutation Groups by Peter J. Cameron Pdf

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 : Unknown
Page : 266 pages
File Size : 49,7 Mb
Release : 1981
Category : Ordered groups
ISBN : LCCN:81016996

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Ordered Permutation Groups by A. M. W. Glass Pdf

Author : Andrew Martin William Glass
Publisher : World Scientific
Page : 326 pages
File Size : 48,8 Mb
Release : 1999
Category : Mathematics
ISBN : 9810234937

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Partially Ordered Groups by Andrew Martin William Glass Pdf

"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

Author : Donald S. Passman
Publisher : Courier Corporation
Page : 160 pages
File Size : 53,5 Mb
Release : 2013-10-03
Category : Mathematics
ISBN : 9780486310916

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Permutation Groups by Donald S. Passman Pdf

Lecture notes by a prominent authority provide a self-contained account of classification theorems. Includes work of Zassenhaus on Frobenius elements and sharply transitive groups, Huppert's theorem, more. 1968 edition.

Author : Meenaxi Bhattacharjee,Rognvaldur G. Moller,Dugald MacPherson
Publisher : Unknown
Page : 220 pages
File Size : 51,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662202050

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Notes on Infinite Permutation Groups by Meenaxi Bhattacharjee,Rognvaldur G. Moller,Dugald MacPherson Pdf

Author : Norbert W Sauer,R.E. Woodrow,B. Sands
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401120807

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Finite and Infinite Combinatorics in Sets and Logic by Norbert W Sauer,R.E. Woodrow,B. Sands Pdf

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.

Author : K. Glazek
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 42,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401599641

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A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences by K. Glazek Pdf

This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).