Let G be a group and let H,K be normal subgroups of G such that H∩K...

Question

Question

Let G be a group and let H,K be normal subgroups of G such that H∩K = {e} and that G = {hk|h ∈ H,k ∈ K}.

(1)Prove that for every h∈H, k∈K we have kh(k^-1)(h^−1) = e in G.

(2) Prove that the group G is isomorphic to H × K.

Hint: For (2), consider the map φ : H ×K → G, defined as φ(h,k) = hk, whereh ∈ H,k ∈ K.

math Advanced-Math

Answer 1

Answer #1

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Answer 2

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