Overview

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.

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Author:   Valentina Grazian ,  Chris Parker
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
ISBN:  

9781470472375

ISBN 10:   1470472376
Pages:   115
Publication Date:   30 June 2025
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Not yet available  
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Table of Contents

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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Valentina Grazian, Universita degli Studi di Padova, Italy. Chris Parker, University of Birmingham, United Kingdom.

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