Domestic intersections in fusion systems.

Let F be a saturated fusion system over a p-group S and let E be a subsystem of F with Aut E (S) = Aut F (S) . We prove that the fusion system F is generated by all E -morphisms and all F -automorphisms of some domestic intersections (called F ∖ E -domestic intersections in the paper) of F . We also get some results about control of fusion in finite groups as applications. [ABSTRACT FROM AUTHOR]