Algebra Vol 1. Groups

Aiming to provide adequate preparation in algebra to prospective teachers and researchers in mathematics and related areas, this book delves into the intricacies of Algebra. Starting with the groups of symmetries of plane configurations, then moving onto study groups (with operators) and their homomorphisms, before diving into the complexities of Sylow's theorems and Abelian groups. All of these topics and many others are richly supported by instructive exercises and purposeful examples, with a focus on the roots of algebra in geometry and number theory. The volume ends with Jordan's classification of finite subgroups of the group of orthogonal transformations of R3.

Table of Contents

• Preface
• Notations
• Preliminaries
• Groups of Plane Symmetries
• Groups and Their Homomorphisms
• Subgroups, Normal Subgroups and Quotient Groups
• Homomorphism Theorems
• Direct and Semidirect Products
• Finite Groups
• Series of Subgroups
• Abelian Groups
• Finite Subgroups of Orthogonal Groups
• Bibliography
• Index