Essential Group Theory
Publisher: Bookboon
Published: 2013
ISBN-13: 9788740303018
Table of contents: title: Introduction; title: Sets and Maps; title: Sets; title: Maps; title: Equivalence Relations and Partitions; title: Modular Arithmetic; title: Groups; title: Binary Operations; title: Groups: Basic Definitions; title: Examples of Groups; title: Subgroups; title: Definition of a Subgroup; title: Cosets; title: Lagrange’s Theorem; title: Generators and Cyclic Groups; title: Orders of Group Elements; title: Generating Sets; title: Cyclic Groups; title: Fermat’s Little Theorem; title: Mappings of Groups; title: Homomorphisms; title: Isomorphisms; title: Normal Subgroups; title: Conjugates and Normal Subgroups; title: Cosets of Normal Subgroups; title: Kernels of Homomorphisms; title: Quotient Groups; title: Products of Cosets; title: Quotient Groups; title: The First Isomorphism Theorem; title: The First Isomorphism Theorem; title: Centres and Inner Automorphisms; title: Group Actions; title: Actions of Groups; title: The Orbit-Stabilizer Theorem; title: Direct Products; title: Direct Products; title: Direct Products of Finite Cyclic Groups; title: Properties of Direct Products; title: Sylow Theory; title: Primes and p-Groups; title: Sylow’s Theorem; title: Presentations of Groups; title: Introduction to Presentations; title: Alphabets and Words; title: Von Dyck’s Theorem; title: Finitely Generated and Finitely Presented Groups; title: Dehn’s Fundamental Algorithmic Problems; title: Free Groups; title: Reduced Words and Free Groups; title: Normal Closure; title: Torsion Free Groups; title: Abelian Groups; title: Commutator Subgroups and Abelianisations; title: Free Abelian Groups; title: Finitely Generated Abelian Groups; title: Generalisations of Abelian Groups; title: Transforming Presentations; title: Tietze Transformations; title: Properties of Tietze Transformations; title: Free Products; title: Free Products; title: A Normal Form for Free Products; title: The Universal Property of Free Products; title: Independence of Presentation; title: Decomposability; title: Free Products With Amalgamation; title: Free Products with Amalgamation; title: Pushouts; title: Independence of Presentation; title: HNN Extensions; title: HNN Extensions; title: Relation to Free Products with Amalgamation; title: The Higman-Neumann-Neumann Embedding Theorem; title: Further Reading; title: Bibliography; title: Index