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<Moderator's note: Moved from General Math to Differential Geometry.>

Let p:E→ B be a covering space with a group of Deck transformations Δ(p). Let b2 ∈ B be a basic point.

Suppose that the action of Δ(p) on p-1(b0) is transitive. Show that for all b ∈ B the action of Δ(p)on p-1(b) is also transitive.

I have to prove that if e ∈ E is such that p(e)=b then p*(π1(E,e)) is a normal subgroup of π1(B,b) but I do not know how to do this, could someone help me please? Thank you very much.

Let p:E→ B be a covering space with a group of Deck transformations Δ(p). Let b2 ∈ B be a basic point.

Suppose that the action of Δ(p) on p-1(b0) is transitive. Show that for all b ∈ B the action of Δ(p)on p-1(b) is also transitive.

I have to prove that if e ∈ E is such that p(e)=b then p*(π1(E,e)) is a normal subgroup of π1(B,b) but I do not know how to do this, could someone help me please? Thank you very much.

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