A Theorem of Tits, Normalizers of Maximal Tori and Fibrewise Bousfield–Kan Completions

We use a theorem of Tits on the presentation of the normalizer of a maximal torus of a connected compact semisimple Lie group in terms of generators and relations to give several equivalent conditions for the splitting of the associated normalizer group extension and interprete them in terms of p-adic fibrewise homotopy theory.