Let H and K be subgroups of a group G satisfying the three properties listed in the
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Let H and K be subgroups of a group G satisfying the three properties listed in the preceding exercise. Show that for each g ∈ G, the expression g = hk for h ∈ H and k E K is unique. Then let each g be renamed (h, k). Show that, under this renaming, G becomes structurally identical (isomorphic) to H x K.
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Uniqueness Suppose that g hk h 1 k 1 for h h 1 H and k k 1 K Then h 1 1 h k 1 k 1 is i...View the full answer
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