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Article Dans Une Revue Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Année : 2020

Reduced fusion systems over $p$-groups with abelian subgroup of index $p$: III

Bob Oliver
  • Fonction : Auteur
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Albert Ruiz
  • Fonction : Auteur

Résumé

We finish the classification, begun in two earlier papers, of all simple fusion systems over finite nonabelian $p$-groups with an abelian subgroup of index $p$. In particular, this gives many new examples illustrating the enormous variety of exotic examples that can arise. In addition, we classify all simple fusion systems over infinite nonabelian discrete $p$-toral groups with an abelian subgroup of index $p$. In all of these cases (finite or infinite), we reduce the problem to one of listing all $\mathbb{F}_pG$-modules (for $G$ finite) satisfying certain conditions: a problem which was solved in the earlier paper by Craven, Oliver, and Semeraro using the classification of finite simple groups.

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hal-03840850 , version 1 (06-11-2022)

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Bob Oliver, Albert Ruiz. Reduced fusion systems over $p$-groups with abelian subgroup of index $p$: III. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2020. ⟨hal-03840850⟩
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