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Article Dans Une Revue Journal of Algebra Année : 2017

Reduced fusion systems over 2-groups of small order

Kasper K. S. Andersen
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Bob Oliver
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Joana Ventura
  • Fonction : Auteur

Résumé

We prove, when $S$ is a $2$-group of order at most $2^9$, that each reduced fusion system over $S$ is the fusion system of a finite simple group and is tame. It then follows that each saturated fusion system over a $2$-group of order at most $2^9$ is realizable. What is most interesting about this result is the method of proof: we show that among $2$-groups with order in this range, the ones which can be Sylow $2$-subgroups of finite simple groups are almost completely determined by criteria based on Bender's classification of groups with strongly $2$-embedded subgroups.

Dates et versions

hal-03840866 , version 1 (06-11-2022)

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Kasper K. S. Andersen, Bob Oliver, Joana Ventura. Reduced fusion systems over 2-groups of small order. Journal of Algebra, 2017. ⟨hal-03840866⟩
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