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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.

Permutation groups. --- Combinatorial analysis. --- Combinatorics --- Algebra --- Mathematical analysis --- Substitution groups --- Group theory

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Ordered algebraic structures --- 512 --- Algebra --- 512 Algebra --- Permutation groups. --- Permutation groups --- Groupes de permutations --- Group theory --- Representations of groups. --- Representations of groups --- Représentations de groupes --- Représentations de groupes --- Groupes finis --- Groupes (algebre) --- Representation

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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.

Combinatorial analysis. --- Permutation groups. --- Ordered algebraic structures --- Discrete mathematics --- 512.54 --- Combinatorial analysis --- Permutation groups --- Substitution groups --- Group theory --- Combinatorics --- Algebra --- Mathematical analysis --- 512.54 Groups. Group theory --- Groups. Group theory --- Groupes de permutations --- Analyse combinatoire

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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.

Permutation groups --- Permutatiegroepen --- Permutation [Groupes de ] --- Group theory. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra

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Ordered algebraic structures --- Ordered algebraic structures. --- Structures algébriques ordonnées. --- Betweenness relations (Mathematics) --- Automorphisms. --- Automorphismes. --- Permutation groups. --- Groupes de permutations. --- Automorphisms --- Permutation groups --- Substitution groups --- Group theory --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- B-sets --- Between relations (Mathematics) --- Betweenness (Mathematics) --- Intermediacy (Mathematics) --- Relations of between (Mathematics) --- Relations of betweenness (Mathematics) --- Relations related to betweenness (Mathematics) --- Set theory --- Symmetry (Mathematics)