arXiv 0803.17462008-03math.GRmath.AT

Equivalences between fusion systems of finite groups of Lie type

Carles Broto, Jesper M. Møller, Bob Oliver

备注：: 20 pages, uses diagrams.sty and xy-pic, second version
发表信息：: J. Amer. Math. Soc. 25 (2012), 1-20
DOI：: 10.1090/S0894-0347-2011-00713-3

英文摘要：

We prove, for certain pairs G,G of finite groups of Lie type, that the p-fusion systems for G and 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 the 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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