David A. Nash

A Friendly Introduction to Group Theory, 2nd Edition (Available on Amazon)

This book is a friendlier, more colloquial textbook for a one-semester course in Abstract Algebra in a liberal arts setting. It would also provide a nice supplement for a more advanced course or any course in group theory with a textbook that is more dense/formal. This book would also make an excellent resource for an independent learner hoping to become familiar with group theory. The textbook covers introductory group theory with an overarching goal of classifying small finite groups. It starts with a chapter of preliminary background material (set theory, basic number theory, induction, etc.) before introducing groups. The rest of the second edition builds up the basic notions and creates a bank of nice examples before proceeding on to more advanced topics. Those topics include:

• subgroups
• quotient groups
• decompositions of groups
• group homomorphisms
• isomorphisms
• automorphism groups
• p-groups
• the Fundamental Theorem of Finite Abelian Groups
• group actions
• conjugation
• Sylow subgroups
• the Sylow theorems

The second edition adds over 75 pages of new material with an entirely new chapter, several new sections, and additional examples and exposition throughout. There are also almost 200 new exercises and an index to help you locate topics quickly.
Click here for a more detailed description including a table of contents.

A Friendly Introduction to Group Theory, 1st Edition (Available on Amazon)

This book is a friendlier, more colloquial textbook for a one-semester course in Abstract Algebra in a liberal arts setting. The textbook covers introductory group theory -- starting with basic notions and examples and moving through subgroups, quotient groups, group homomorphisms, and isomorphisms. If you (or your students) are struggling with a textbook that is more dense/formal, then this would make a great supplement to your course. This book is also well-designed as a resource for an independent learner hoping to become familiar with group theory on their own.
Click here for a more detailed description including a table of contents.