Equivalences between fusion systems of finite groups of Lie typeReport as inadecuate

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1 Departament de Matemàtiques Barcelona 2 Matematisk Institut 3 LAGA - Laboratoire Analyse, Géométrie et Applications

Abstract : We prove, for certain pairs G,G- of finite groups of Lie type, that the $p$-fusion systems F pG and F pG- 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=Hq and G-=Hq- 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.

Mots-clés : groupes de type Lie systèmes de fusion espaces classifiants p-complétion

Author: Carles Broto - Jesper Møller - Bob Oliver -

Source: https://hal.archives-ouvertes.fr/


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