first post

This blog will be notes on group theory. You should know a little bit about groups and what they are to read this.

The focus is on finite simple groups. Sometimes definitions and theorems are stated without proof, this means the reader should fill it in. Please tell me if you find mistakes or want to make suggestions.

$$G \to G/[G,G]$$

• Amazingly good intro group theory: GroupProps: Getting Started 
• McKay's great proof of Cauchy's theorem 

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 Not underlined means it's (should be..) "revision"

Section 1:

1. Noethers Isomorphism theorems.
2. Automorphisms (Inner and Outer).
3. Group actions and the orbit-stabilizer theorem.
4. Normalizers and the conjugacy-class equation
5. Sylow p-groups (uses orbits)
6. Commutator subgroups.
7. Series. Composition Series. Central Series. Jordan-Holder.
8. ABC.
9. Optimal series for solvable groups
10. Optimal series for nilpotent groups
11. Structure of Nilpotent: product of p-groups
12. Halls theorem
13. Structure of Solvable: Sylow-bases

Section 2:

1.