Course:

Abstract AlgebraLearn 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

Course Description

Abstract Algebra deals with groups, rings, fields, and modules. These are abstract structures which appear in many different branches of mathematics, including geometry, number theory, topology, and more. They even appear in scientific topics such as quantum mechanics.