\(E_8\) is a totally \(N\)-determined 5-compact group (Q2707517)

Let \(p\) be a prime and let \(X\) be a \(p\)-compact group with its maximal torus normalizer \(j:N\to X\). In this paper, the author studies whether \(X\) is \(N\)-determined or not for the case \(p=5\). Let \(E_8\) be the exceptional compact Lie group of rank \(8\). Previous works of several authors show that a \(5\)-compact group \(X\) is totally \(N\)-determined as soon as its maximal torus normalizer \(j:N\to X\) has no factor isomorphic to the maximal torus normalizer of \(E_8\). So the missing point in the classification of \(5\)-compact groups is the case of \(E_8\) and the author fills this point in this paper. In particular, he proves that the exceptional Lie group \(E_8\) is a totally \(N\)-determined \(5\)-compact group. As its corollary, he also obtains that every \(5\)-compact group is totally \(N\)-determined.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00041].