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# Fundamentals

The axioms, subgroups, abelian groups, homomorphisms, and quotient groups.

From the basic axioms to quotient groups, this chapter explores the fundamentals of Group Theory through beautiful problems and rigorous explanations.

This chapter covers:

- The group axioms and examples of groups
- Subgroups
- Abelian groups
- Homomorphisms
- Quotient groups

You'll build the same foundations as in a traditional Group Theory course, but you'll do it quicker, through more interesting problems, and with carefully crafted solutions and feedback on your answers. **Dive in!**

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