Let H and K be subgroups of a group G. (a) Define HK = {hk | he H, ke K}. Show that if K is normal in G, then HK ≤G. (b) Show that if H and K are normal in G, then HK is normal in G. (c) Show that H is normal in G if and only if xy € H ⇒ yx € H, where x, y € G.

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