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Reading Questions 15.3 Reading Questions

1.

State Sylow's First Theorem.

2.

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

3.

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

4.

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

5.

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