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Author: Norman Biggs
Publisher: Cambridge University Press
ISBN: 0521222877
Category : Mathematics
Languages : en
Pages : 153
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Book Description
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: Norman Biggs
Publisher: Cambridge University Press
ISBN: 0521222877
Category : Mathematics
Languages : en
Pages : 153
Get Book
Book Description
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: Norman L. Biggs
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 152
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Book Description
The subject of this book is the action of permutation groups on sets associated with combinatorial structures.
Author: Peter J. Cameron
Publisher: Cambridge University Press
ISBN: 9780521653787
Category : Mathematics
Languages : en
Pages : 236
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Book Description
This book summarizes recent developments in the study of permutation groups for beginning graduate students.
Author: Meenaxi Bhattacharjee
Publisher: Springer Science & Business Media
ISBN: 9783540649656
Category : Mathematics
Languages : en
Pages : 224
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Book Description
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
Publisher: Springer Science & Business Media
ISBN: 1461207312
Category : Mathematics
Languages : en
Pages : 360
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Book Description
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: Cheryl E. Praeger
Publisher: Cambridge University Press
ISBN: 131699905X
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Permutation groups, their fundamental theory and applications are discussed in this introductory book. It focuses on those groups that are most useful for studying symmetric structures such as graphs, codes and designs. Modern treatments of the O'Nan–Scott theory are presented not only for primitive permutation groups but also for the larger families of quasiprimitive and innately transitive groups, including several classes of infinite permutation groups. Their precision is sharpened by the introduction of a cartesian decomposition concept. This facilitates reduction arguments for primitive groups analogous to those, using orbits and partitions, that reduce problems about general permutation groups to primitive groups. The results are particularly powerful for finite groups, where the finite simple group classification is invoked. Applications are given in algebra and combinatorics to group actions that preserve cartesian product structures. Students and researchers with an interest in mathematical symmetry will find the book enjoyable and useful.
Author: Peter J. Cameron
Publisher: Cambridge University Press
ISBN: 0521388368
Category : Mathematics
Languages : en
Pages : 172
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Book Description
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: Gregory Butler
Publisher: Springer
ISBN: 9783540549550
Category : Computers
Languages : en
Pages : 244
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Book Description
This is the first-ever book on computational group theory. It provides extensive and up-to-date coverage of the fundamental algorithms for permutation groups with reference to aspects of combinatorial group theory, soluble groups, and p-groups where appropriate. The book begins with a constructive introduction to group theory and algorithms for computing with small groups, followed by a gradual discussion of the basic ideas of Sims for computing with very large permutation groups, and concludes with algorithms that use group homomorphisms, as in the computation of Sylowsubgroups. No background in group theory is assumed. The emphasis is on the details of the data structures and implementation which makes the algorithms effective when applied to realistic problems. The algorithms are developed hand-in-hand with the theoretical and practical justification.All algorithms are clearly described, examples are given, exercises reinforce understanding, and detailed bibliographical remarks explain the history and context of the work. Much of the later material on homomorphisms, Sylow subgroups, and soluble permutation groups is new.
Author: Andrew Martin William Glass
Publisher: Cambridge University Press
ISBN: 0521241901
Category : Mathematics
Languages : en
Pages : 333
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Book Description
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: Richard Arratia
Publisher: European Mathematical Society
ISBN: 9783037190005
Category : Mathematics
Languages : en
Pages : 380
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Book Description
This book explains similarities in asymptotic behavior as the result of two basic properties shared by the structures: the conditioning relation and the logarithmic condition. The discussion is conducted in the language of probability, enabling the theory to be developed under rather general and explicit conditions; for the finer conclusions, Stein's method emerges as the key ingredient.
