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Pré-Publication, Document De Travail Année : 2008

Equivalences between fusion systems of finite groups of Lie type

Résumé

We prove, for certain pairs G,G' of finite groups of Lie type, that the $p$-fusion systems F_p(G) and F_p(G') are equivalent. In other words, there is an isomorphism between a Sylow p-subgroup of G and one of G' which preserves p-fusion. This occurs, for example, when G=H(q) and G'=H(q') for a simple Lie "type" H, and q and q' are prime powers, both prime to p, which generate the same closed subgroup of p-adic units. Our proof uses homotopy theoretic properties of the p-completed classifying spaces of G and G', and we know of no purely algebraic proof of this result.
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Dates et versions

hal-00308742 , version 1 (01-08-2008)

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  • HAL Id : hal-00308742 , version 1

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Carles Broto, Jesper Møller, Bob Oliver. Equivalences between fusion systems of finite groups of Lie type. 2008. ⟨hal-00308742⟩
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