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Author : Cheryl E. Praeger,Csaba Schneider
Publisher : London Mathematical Society Le
Page : 338 pages
File Size : 48,8 Mb
Release : 2018-05-03
Category : Mathematics
ISBN : 9780521675062
Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.
Author : Peter J. Cameron
Publisher : Cambridge University Press
Page : 236 pages
File Size : 49,6 Mb
Release : 1999-02-04
Category : Mathematics
ISBN : 0521653789
This book summarizes recent developments in the study of permutation groups for beginning graduate students.
Author : Helmut Wielandt
Publisher : Academic Press
Page : 124 pages
File Size : 45,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483258294
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.
Author : Meenaxi Bhattacharjee,Dugald Macpherson,Rögnvaldur G. Möller,Peter M. Neumann
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 43,6 Mb
Release : 1998-11-20
Category : Mathematics
ISBN : 3540649654
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 : John D. Dixon,Brian Mortimer
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207313
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 : Norman Biggs,A. T. White
Publisher : Cambridge University Press
Page : 153 pages
File Size : 50,5 Mb
Release : 1979-08-16
Category : Mathematics
ISBN : 9780521222877
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.
Author : A. Kerber
Publisher : Springer
Page : 186 pages
File Size : 43,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540370048
Author : Andrew Martin William Glass
Publisher : Cambridge University Press
Page : 333 pages
File Size : 40,8 Mb
Release : 1981
Category : Mathematics
ISBN : 9780521241908
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 : Norman L. Biggs,A. T. White
Publisher : Unknown
Page : 152 pages
File Size : 41,5 Mb
Release : 1979
Category : Combinatorial analysis
ISBN : OCLC:472109769
The subject of this book is the action of permutation groups on sets associated with combinatorial structures.
Author : Adalbert Kerber
Publisher : Unknown
Page : 190 pages
File Size : 42,7 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015046547645
Author : Donald S. Passman
Publisher : Courier Corporation
Page : 160 pages
File Size : 42,7 Mb
Release : 2013-10-03
Category : Mathematics
ISBN : 9780486310916
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 : A. Kerber
Publisher : Unknown
Page : 188 pages
File Size : 45,9 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662188813
Author : W.C. Holland
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 55,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334439
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 : Cameron Peter J
Publisher : Unknown
Page : 231 pages
File Size : 53,5 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362768
This book summarizes recent developments in the study of permutation groups for beginning graduate students.
Author : A. M. W. Glass
Publisher : Unknown
Page : 266 pages
File Size : 41,7 Mb
Release : 1981
Category : Electronic
ISBN : 1107045819