ordered permutation groups london mathematical society lecture note series

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Ordered Permutation Groups

Author : Andrew Martin William Glass
ISBN : 9780521241908
Genre : Mathematics
File Size : 61. 84 MB
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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.

Permutation Groups And Combinatorial Structures

Author : Norman L. Biggs
ISBN : 9780521222877
Genre : Mathematics
File Size : 58. 33 MB
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The subject of this book is the action of permutation groups on sets associated with combinatorial structures. Each chapter deals with a particular structure: groups, geometries, designs, graphs and maps respectively. A unifying theme for the first four chapters is the construction of finite simple groups. In the fifth chapter, a theory of maps on orientable surfaces is developed within a combinatorial framework. This simplifies and extends the existing literature in the field. The book is designed both as a course text and as a reference book for advanced undergraduate and graduate students. A feature is the set of carefully constructed projects, intended to give the reader a deeper understanding of the subject.

Ordered Groups And Infinite Permutation Groups

Author : W.C. Holland
ISBN : 9781461334439
Genre : Mathematics
File Size : 73. 20 MB
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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.

London Mathematical Society Lecture Note Series

Author :
ISBN : UCAL:B5111463
Genre :
File Size : 69. 13 MB
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Groups Modules And Model Theory Surveys And Recent Developments

Author : Manfred Droste
ISBN : 9783319517186
Genre : Mathematics
File Size : 65. 97 MB
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This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.

Surveys In Combinatorics 1997

Author : R. A. Bailey
ISBN : 0521598400
Genre : Mathematics
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The invited lectures given at the 16th. British Combinatorial Conference, July 1997 at Queen Mary and Westfield College.

London Mathematical Society Lecture Note Series

Author : C. M. Campbell
ISBN : UCAL:B5111484
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File Size : 53. 89 MB
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Notes On Infinite Permutation Groups

Author : Meenaxi Bhattacharjee
ISBN : 9783540498131
Genre : Mathematics
File Size : 67. 25 MB
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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.

Higher Operads Higher Categories

Author : Tom Leinster
ISBN : 0521532159
Genre : Mathematics
File Size : 54. 76 MB
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Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. The heart of this book is the language of generalized operads. This is as natural and transparent a language for higher category theory as the language of sheaves is for algebraic geometry, or vector spaces for linear algebra. It is introduced carefully, then used to give simple descriptions of a variety of higher categorical structures. In particular, one possible definition of n-category is discussed in detail, and some common aspects of other possible definitions are established. This is the first book on the subject and lays its foundations. It will appeal to both graduate students and established researchers who wish to become acquainted with this modern branch of mathematics.

Ergodic Theory And Topological Dynamics Of Group Actions On Homogeneous Spaces

Author : M. Bachir Bekka
ISBN : 0521660300
Genre : Mathematics
File Size : 36. 17 MB
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This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.

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