and are subgroups of G then which of the following is always a subgroup of G
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Give an example of a group G and two subgroups H and K such that HK is a subgroup of G but neither H nor K are normal subgroups of G. h = h1 ∈ HK and k = 1k ∈ HK and since HK is closed under products, we deduce kh ∈ HK. Thus we have KH ⊆ HK. ... Hence if HK is a subgroup of G, then HK = KH.
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