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

Häftad, Engelska, 2025

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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.

Produktinformation

Utgivningsdatum2025-06-30
Mått178 x 254 x undefined mm
FormatHäftad
SpråkEngelska
SerieMemoirs of the American Mathematical Society
Antal sidor115
FörlagAmerican Mathematical Society
ISBN9781470472375

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Algebra inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Chapters1. Introduction and main results2. General group theoretical results3. Maximal class $p$-groups4. Representations of groups with a cyclic Sylow $p$-subgroup5. A primer on fusion systems6. Fusion systems on $p$-groups of maximal class: Generalities7. Essential subgroups in exceptional maximal class $p$-groups8. The structure of $\gamma _1(S)$ when $\gamma _1(S)$ is $\mathcal {F}$-essential and $S$ is not exceptional9. The structure of $\gamma _1(S)$ when $\gamma _1(S)$ is $\mathcal {F}$-essential and $S$ is exceptional10. Locating $\mathcal {F}$-essential subgroups in groups of maximal class I11. Locating $\mathcal {F}$-essential subgroups in groups of maximal class II12. The saturated fusion systems on exceptional maximal class groups: The proof of Theorem B13. The saturated fusion systems on non-exceptional maximal class groups14. The proofs of Theorems A and C15. A series of examples with non-abelian $2$-step centralizerA. Saturated fusion systems on maximal class $p$-groups with $\gamma _1(S)$ abelianB. The saturated fusion systems on maximal class $3$-groupsC. Computer code