F U N D a M E N T a Mathematicae N -determined 2-compact Groups. Ii

This is the second part of a paper about the classification of 2-compact groups. In the first part we set up a general classification procedure and applied it to the simple 2-compact groups of the A-family. In this second part we deal with the other simple Lie groups and with the exotic simple 2-compact group DI(4). We show that all simple 2-compact groups are uniquely N -determined and conclude that all connected 2-compact groups are uniquely N -determined. This means that two connected 2-compact groups are isomorphic if their maximal torus normalizers are isomorphic and that the automorphisms of a connected 2-compact group are determined by their effect on a maximal torus. As an application we confirm the conjecture that any connected 2-compact group is the product of a compact Lie group with copies of the exceptional 2-compact group DI(4).