Let H and K be subgroups of a group G. Prove that gH ? gK is a coset of H ? K in G.
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First, we need to show that gH ∩ gK is non-empty. - Let x be an element in gH ∩ gK. Then, x = gh = gk for some h in H and k in K. - This implies that h = g^-1k g, which means that h is in gKg^-1 (since k and g are in K and G respectively). - Therefore, Show more…
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