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

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The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
Valentina Grazian, Universita degli Studi di Padova, Italy. Chris Parker, University of Birmingham, United Kingdom.
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
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