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$N$-determined 2-compact groups. II

Tom 196 / 2007

Jesper M. Møller Fundamenta Mathematicae 196 (2007), 1-90 MSC: 55Q45, 55P15. DOI: 10.4064/fm196-1-1

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 ${\rm DI}(4)$.

Autorzy

  • Jesper M. MøllerMatematisk Institut
    Universitetsparken 5
    DK-2100 København, Denmark
    e-mail

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