Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

Streszczenie

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 $\rm A$-family. In this second part we deal with the other simple Lie groups and with the exotic simple $2$-compact group ${\rm DI}(4)$. 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 normalizer s 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 ${\rm DI}(4)$.