J.M. Moller: Normalizers of maximal tori
Normalizers and p-normalizers of maximal tori in p-compact groups can be
characterized by the Euler characteristic of the associated
homogeneous spaces. Applied to centralizers of elementary abelian
p-groups these criteria show that
the normalizer of a maximal torus of the
centralizer is given by the centralizer of a preferred homomorphism
to the normalizer of the maximal torus; i.e. that ``normalizer'' commutes with
``centralizer''.