Group Theory (Dover Books on Mathematics)

Book Details

• Author: W. R. Scott

• Publisher: Dover

• Edition: New Edition

• Binding: Paperback

• Pages: 512

• Release Date: 23-06-2010

• ISBN: 9780486653778

• Dimensions: 8.5 x 5.4 x 1.1 inches

• Languages: English

About the Book

Group Theory by W. R. Scott is a well-organized and clearly written undergraduate-level textbook that provides a comprehensive introduction to group theory, an essential area of modern mathematics. The book is designed to offer a rigorous exploration of both finite and infinite groups, while also developing a substantial portion of their superstructure. It is ideal for students looking for an accessible, yet thorough treatment of group theory that includes proofs, examples, and a wide range of exercises.

Key Features:

• Coverage of Standard Theorems: The book covers most of the basic theorems in group theory, offering detailed proofs and explanations. Topics include:

  • Isomorphism Theorems

  • Direct Sums

  • p-Groups and p-Subgroups

  • Free Groups and Free Products

  • Permutation Groups

  • Transformations and Subgroups

  • Abelian Groups

  • Supersolvable Groups

  • Extensions

  • Representations

• Further Theorems: In addition to the standard topics, the book explores more advanced results, including:

  • Infinite symmetric and alternating groups

  • Products of subgroups

  • The multiplicative group of a division ring

  • FC groups

• Exercises: The book contains over 500 exercises of varying difficulty, allowing students to test their understanding and deepen their mastery of group theory. The exercises are well-suited for self-study and are integrated with the material for practice and review.

• Self-Contained: Except for the later chapters (which require some knowledge of linear algebra, polynomials, algebraic integers, and elementary number theory), the text is largely self-contained, making it suitable for a wide range of students in mathematics.

• Ideal for Text or Reference: This book can be used as both a textbook for coursework and a reference guide for those exploring group theory in greater depth.

Why This Book is Important:

Group Theory by W. R. Scott is a classic and highly regarded introduction to group theory. Its clarity and thoroughness make it an excellent choice for undergraduate students studying abstract algebra. The book's well-balanced approach, combining theory with practical exercises, ensures that students gain both the theoretical knowledge and problem-solving skills required in this important field of mathematics.

Who Should Read This Book:

• Undergraduate Students: Ideal for students studying mathematics, particularly those focused on algebra, group theory, or abstract mathematics.

• Self-Learners: The book's structure and abundance of exercises make it suitable for independent study.

• Instructors: A valuable resource for teaching group theory, providing a wealth of material for lectures, assignments, and exams.

• Mathematics Enthusiasts: Anyone interested in the foundational aspects of group theory will find this text a thorough and valuable reference.