Saturated Fusion Systems on $p$-Groups of Maximal Class

Chapters
1. Introduction and main results
2. General group theoretical results
3. Maximal class $p$-groups
4. Representations of groups with a cyclic Sylow $p$-subgroup
5. A primer on fusion systems
6. Fusion systems on $p$-groups of maximal class: Generalities
7. Essential subgroups in exceptional maximal class $p$-groups
8. The structure of $\gamma _1(S)$ when $\gamma _1(S)$ is $\mathcal {F}$-essential and $S$ is not exceptional
9. The structure of $\gamma _1(S)$ when $\gamma _1(S)$ is $\mathcal {F}$-essential and $S$ is exceptional
10. Locating $\mathcal {F}$-essential subgroups in groups of maximal class I
11. Locating $\mathcal {F}$-essential subgroups in groups of maximal class II
12. The saturated fusion systems on exceptional maximal class groups: The proof of Theorem B
13. The saturated fusion systems on non-exceptional maximal class groups
14. The proofs of Theorems A and C
15. A series of examples with non-abelian $2$-step centralizer
A. Saturated fusion systems on maximal class $p$-groups with $\gamma _1(S)$ abelian
B. The saturated fusion systems on maximal class $3$-groups
C. Computer code