Chapter 5: Quotient groups | Essence of Group Theory

Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory!

In fact, the concept of quotient groups is one way to define modular arithmetic formally, which allows us to prove a lot of number theory theorems once we draw parallels between group theory and number theory. For example, Fermat's little theorem and Euler's totient theorem are just corollaries of the Lagrange's theorem introduced in Chapter 3 of the video series.

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