Topics in Group Theory (Springer Undergraduate Mathematics Series)
Edition: 1 edition
Publisher: Springer
Published: June 16, 2000
Language: eng
Format: Paperback
Number of pages: 256
ISBN-13: 9781852332358
Subjects: Groups & group theory; Theory Of Groups; Mathematics; Science/Mathematics; Algebra; Mathematics / Algebra / General; Mathematics / Group Theory; Symmetry; Group Theory
First sentence: In this chapter we recap basic definitions and results from the theory of groups, up to and including Lagrange's Theorem.
Description: The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed to support a reader engaged in a first serious group theory course, or a mathematically mature reader approaching the subject for the first time, this book reviews the essentials. It recaps the basic definitions and results, up to and including Lagrange's Theorem, and then continues to explore topics such as the isomorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" takes the basic theory and plays with it to obtain an assortment of results that will show a little of what can be done with the theoretical machinery. Adopting the slightly irreverent tone of Geoff Smith's previous book, Introductory Mathematics: Algebra and Analysis, this book is a key reference that will both stimulate and entertain its readers.