Oligomorphic Permutation Groups
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Oligomorphic Permutation Groups
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Author : Peter J. Cameron
language : en
Publisher: Cambridge University Press
Release Date : 1990-06-29
Oligomorphic Permutation Groups written by Peter J. Cameron and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-06-29 with Mathematics categories.
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.
Oligomorphic Permutation Groups
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Author : Peter Jephson Cameron
language : en
Publisher:
Release Date : 2014-05-14
Oligomorphic Permutation Groups written by Peter Jephson Cameron and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
The study of permutation 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. They are precisely those structures which are determined by first-order logical axioms together with the assumption of countability. This book concerns such structures, their substructures and their automorphism groups. A wide range of techniques are used: group theory, combinatorics, Baire category and measure among them. The book arose from lectures given at a research symposium and retains their informal style, whilst including as well many recent results from a variety of sources. It concludes with exercises and unsolved research problems.
Permutation Groups
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Author : Peter J. Cameron
language : en
Publisher: Cambridge University Press
Release Date : 1999-02-04
Permutation Groups written by Peter J. Cameron and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-04 with Mathematics categories.
This book summarizes recent developments in the study of permutation groups for beginning graduate students.
Notes On Infinite Permutation Groups
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Author : Meenaxi Bhattacharjee
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-11-20
Notes On Infinite Permutation Groups written by Meenaxi Bhattacharjee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-20 with Mathematics categories.
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.
Automorphisms Of First Order Structures
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Author : Richard Kaye
language : en
Publisher:
Release Date : 2023
Automorphisms Of First Order Structures written by Richard Kaye and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Automorphisms categories.
This collection of essays discusses a range of topics linking infinite permutation group theory and model theory. Topics covered include: oligomorphic permutation groups and omega-categorical structures; totally categorical structures and covers; and Jordan groups.
Finite Permutation Groups
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Author : Helmut Wielandt
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Finite Permutation Groups written by Helmut Wielandt and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Permutation Groups
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Author : John D. Dixon
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Permutation Groups written by John D. Dixon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Ordered Permutation Groups
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Author : Andrew Martin William Glass
language : en
Publisher: Cambridge University Press
Release Date : 1981
Ordered Permutation Groups written by Andrew Martin William Glass and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
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.
Notes On Infinite Permutation Groups
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Author : Meenaxi Bhattacharjee
language : en
Publisher: Springer
Release Date : 2006-11-14
Notes On Infinite Permutation Groups written by Meenaxi Bhattacharjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
Ordered Groups And Infinite Permutation Groups
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Author : W.C. Holland
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Ordered Groups And Infinite Permutation Groups written by W.C. Holland and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
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.