is well defined transformation. Then it is clear that ∀g ∈ G is indeed an action on X 1 . Consequently, the G-action on X 1 is well defined, indicating the correspondence of g → g•. Thus for any x ′ , y ′ ∈ X 1 , g ∈ G act as a transformation group on X 1 , that ω 2 (g • x ′ ) = ω 2 (x ′ ). Therefore, the correspondence of g → g• is actually a homomorphism, which is also surjective. As G act transitively on any fibre of ω 2 , the first statement is proved. (ii).From discussion above, suppose ω 2 is normal, that is to say Deck(ω 2 ) act transitively on fibres of X 0 . Then, with unique lifting, one can find a homomorphism ρ : G → G 2 , where