Radu Stancu
Université de Picardie Jules Verne, France

Fusion systems are a generalization of the conjugation action of a finite group on one of its Sylow $p$-subgroups. We define the fusion system on a pro-$p$-group, and give the saturation axioms in this context. We show that classical theorems as Alperin fusion theorem also hold for saturated fusion systems on pro-$p$-groups. In particular, one can show that morphisms in a saturated fusion system on an uniform pro-$p$-group can be written as a composition of restrictions of a finite number of automorphisms. This is a joint work with Peter Symonds.