We prove that for any compact simple Lie group G and any nonidentity element g of G the subset of h ∈ G, for which g, h topologically generate G, is nonempty and Zariski open in G. A connected compact Lie group G satisfies 1.5-generation property iff it is simple or abelian. Any compact simple Lie group G has a conjugacy class C such that for every nontrivial elements g_1,g_2 of G there exists y ∈ C so that = = G. In particular, the generating graph of G has diameter 2.
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