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An Introduction to Group Theory

In this video, we cover the basics of group theory. We start with examples like the dihedral group and the symmetric group. After this we discuss subgroups and Lagrange's theorem. Then we go over the definition of a group homomorphism and of quotient groups, and apply the fundamental theorem of homomorphisms to some examples. In the next chapter, we study group actions and topics like the Orbit-Stabilizer theorem, the Orbit-Decomposition formula, the Class equation and Burnside's lemma. Finally we take a look at p-groups and the Sylow theorems, and talk about nilpotent groups and the fundamental theorem of finite abelian groups. Sources Gallian, Contemporary Abstract Algebra Lang, Algebra Dummit and Foote, Abstract Algebra 00:00 1. What is a group? 04:40 2. Subgroups and Lagrange's Theorem 08:16 3. Homomorphisms and Quotient Groups 17:19 4. Group Actions 24:12 5. Sylow Theorems Math animations created using Manim