N-groups and fusion systems

We classify all saturated 2-fusion systems that are N-systems: that is those systems all of whose local subsystems are solvable, subject to one of the two possible notions of solvability. We also use the result on fusion systems to give a new proof of Thompson's theorem on N-groups; indeed we give a new proof of the theorem determining all finite groups in which all 2-locals are solvable.