Abstract Algebra: Theory and Applications

State Sylow’s First Theorem.

How many groups are there of order $69\text{?}$ Why?

Give two descriptions, fundamentally different in character, of the normalizer of a subgroup.

Suppose that $G$ is an abelian group. What is the commutator subgroup of $G\text{,}$ and how do you know?

What’s all the fuss about Sylow’s Theorems?