Group Theory

Fülszöveg

GROUP THEORY, a basic subject in mathematics, is handled here with simple and elementary tools. Intended to give a self-contained introduction to the subject, this volume develops group theory from its axiomatic beginnings to somé of the recent deep theory, such as the Thompson theorem on normál p-complements and the Hirsch-Plotkin radical. The chapters progress in difficulty, but are independent of one another as much as possible, permitting the reader to follow one topic in detail with minimum reference to other chapters. Contents I FUNDAMENTAL CONCEPTS Semigroups and Groups • Subgroups and Cosets • Homomorphisms and Normál Subgroups • Cyclic Groups • Generators and Defining Relations; Free Groups • Cartesian and Direct Products • The Frattini Subgroup • Varieties II ABELIAN GROUPS Elementary Facts About Abelian Groups • Locally Cyclic Groups • Finitely Generated Abelian Groups • Rank and Linear Independence • Pure Subgroups; Direct Sums of Cyclic p-Groups • Direct Sums of Cyclic... Tovább

Fülszöveg

GROUP THEORY, a basic subject in mathematics, is handled here with simple and elementary tools. Intended to give a self-contained introduction to the subject, this volume develops group theory from its axiomatic beginnings to somé of the recent deep theory, such as the Thompson theorem on normál p-complements and the Hirsch-Plotkin radical. The chapters progress in difficulty, but are independent of one another as much as possible, permitting the reader to follow one topic in detail with minimum reference to other chapters. Contents I FUNDAMENTAL CONCEPTS Semigroups and Groups • Subgroups and Cosets • Homomorphisms and Normál Subgroups • Cyclic Groups • Generators and Defining Relations; Free Groups • Cartesian and Direct Products • The Frattini Subgroup • Varieties II ABELIAN GROUPS Elementary Facts About Abelian Groups • Locally Cyclic Groups • Finitely Generated Abelian Groups • Rank and Linear Independence • Pure Subgroups; Direct Sums of Cyclic p-Groups • Direct Sums of Cyclic Groups; Free Abelian Groups • Divisible Groups • Basic Subgroups III IMPORTANT SUBGROUPS, MAPPINGS, CONSTRUCTIONS, AND FAMILIES OF GROUPS Commutators, Conjugates, Center, Centralizer, Normalizer, and Related Topics • Endomorphisms and Automorphisms • Operator Groups, Modules, and Vector Spaces • Semidirect Products • The Wreath Product • The Normál Structure of Groups • The Symmetric and Alternating Groups • Linear Groups IV SYLOW THEOREMS AND GENERALIZATIONS Sylow Theory • Applications of Sylow Theory • The Transfer • Two Theorems on Transfer • Normál p-Complements • A Further Result on Sylow Vissza