1. What is the normal subgroup of a semi-direct product Isom(H) = O(H°) ∝ H° ?

2. Definition of semi-direct product is given below:
π : G --> Aut(H)
G ∝ H = {(g, h) : g ∈ G, h ∈ H} with group operation (g₁, h₁),(g₂, h₂) = (g₁g₂, π(g₁), h₁, h₂)
If we compare it with example (A₁, b₁),(A₂, b₂) = (A₁A₂, A, b₂ + b₁), what is π ?

3. Please show that Z'(G, π) is a real vector space and B'(G, π) is a subspace of Z'(G, π).

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