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Suppose that H is a normal subgroup of G and K is any subgroup of G....

Suppose that H is a normal subgroup of G and K is any subgroup of G. Define HK = {hk : h ? H, k ? K}.

(a) Show that HK is a subgroup of G.

(b) Does the conclusion of (a) continue to hold if H is not normal in G? Justify

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