Abstract Algebra


Group Definition (Quick)

Learn the definition of a group - one of the most fundamental ideas from abstract algebra.

One of the core concepts in Abstract Algebra is the group. This is a way to generalize an abstract idea. How do you mathematically describe something (almost anything) that has the following characteristics?

A group...
▪ Is a set of elements
▪ Has an operation (called the group operation)
▪ Is closed under the operation
▪ Has inverse elements
▪ Has an identity element
▪ Has associativity

We made this quick video to introduce you to the textbook definition of the group, but if you are intrigued and want to know more, visit the Expanded, Detailed explanation of the group next. Find more lessons and resources below.

Course Page


Abstract Algebra Textbook
Abstract Algebra by Dummit & Foote is a standard textbook used by colleges and universities. It is extremely well written with lots of examples and exercises. It covers all the topics for a solid first course in Abstract Algebra. We use this on occasion as a reference for inspiration or reference. Highly recommended!