Cherlin S Conjecture For Finite Primitive Binary Permutation Groups
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Cherlin S Conjecture For Finite Primitive Binary Permutation Groups
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Author : Nick Gill
language : en
Publisher: Springer Nature
Release Date : 2022-06-17
Cherlin S Conjecture For Finite Primitive Binary Permutation Groups written by Nick Gill and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-17 with Mathematics categories.
This book gives a proof of Cherlin’s conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan’s theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. The first part gives a full introduction to Cherlin’s conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest to a wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.
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.
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.
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.
Homogeneous Ordered Graphs Metrically Homogeneous Graphs And Beyond
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Author : Gregory Cherlin
language : en
Publisher: Cambridge University Press
Release Date : 2022-07-07
Homogeneous Ordered Graphs Metrically Homogeneous Graphs And Beyond written by Gregory Cherlin 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 2022-07-07 with Mathematics categories.
The second of two volumes presenting the state of the art in the classification of homogeneous structures and related problems in the intersection of model theory and combinatorics. It extends the results of the first volume to generalizations of graphs and tournaments with additional binary relations. An appendix explores open problems.
Complexity Of Infinite Domain Constraint Satisfaction
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Author : Manuel Bodirsky
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-10
Complexity Of Infinite Domain Constraint Satisfaction written by Manuel Bodirsky 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 2021-06-10 with Mathematics categories.
Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.
Regular Subgroups Of Primitive Permutation Groups
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Author : Martin W. Liebeck
language : en
Publisher:
Release Date : 2009
Regular Subgroups Of Primitive Permutation Groups written by Martin W. Liebeck and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with MATHEMATICS categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2002
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Finite Structures With Few Types
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Author : Gregory L. Cherlin
language : en
Publisher: Princeton University Press
Release Date : 2003
Finite Structures With Few Types written by Gregory L. Cherlin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4-tuples. Primitive permutation groups of this type have been classified by Kantor, Liebeck, and Macpherson, using the classification of the finite simple groups. Building on this work, Gregory Cherlin and Ehud Hrushovski here treat the general case by developing analogs of the model theoretic methods of geometric stability theory. The work lies at the juncture of permutation group theory, model theory, classical geometries, and combinatorics. The principal results are finite theorems, an associated analysis of computational issues, and an "intrinsic" characterization of the permutation groups (or finite structures) under consideration. The main finiteness theorem shows that the structures under consideration fall naturally into finitely many families, with each family parametrized by finitely many numerical invariants (dimensions of associated coordinating geometries). The authors provide a case study in the extension of methods of stable model theory to a nonstable context, related to work on Shelah's "simple theories." They also generalize Lachlan's results on stable homogeneous structures for finite relational languages, solving problems of effectivity left open by that case. Their methods involve the analysis of groups interpretable in these structures, an analog of Zilber's envelopes, and the combinatorics of the underlying geometries. Taking geometric stability theory into new territory, this book is for mathematicians interested in model theory and group theory.
Complexity Of Infinite Domain Constraint Satisfaction
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Author : Manuel Bodirsky
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-10
Complexity Of Infinite Domain Constraint Satisfaction written by Manuel Bodirsky 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 2021-06-10 with Computers categories.
Introduces the universal-algebraic approach to classifying the computational complexity of constraint satisfaction problems.