This is the first post of the Introduction to Abstract Algebra series, and we will start with groups. In this very first post, we will introduce the basic concepts in group theory, starting from mappings, equivalent relations, partitions, and extending to groups and homomorphisms. We will also encounter the first important theorem, the Lagrange's theorem.
This is the second post of the Introduction to Abstract Algebra series. In the first post, we introduce the basic concepts of groups. In this post, we will introduce four isomorphism theorems. But first of all, we need to define normal groups.
This is the third post of the Introduction to Abstract Algebra series. In this post, we will introduce group actions, which give rise to the Cayley's Theorem and the class equation.
This is the fourth post of the Introduction to Abstract Algebra series. In the first three posts, we are acquainted with the fundamental concepts and techniques in group theory. In this post, we will introduce the Sylow theorems.
This is the fifth post of the Introduction to Abstract Algebra series, and the last post about group theory. In this post, we will finalize our tool box by introducing automorphisms, direct products, and semi-direct products. Finally, we can start to harvest our efforts with group classification.