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math8
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Let H be normal in G, H cyclic. Show any subgroup K of H is normal in G.
I was thinking about using the fact that subgroups of cyclic groups are cyclic, and that subgroups of cyclic groups are (fully)Characteristic (is that true?). Then we would have
K char in H and H normal in G.
Hence K normal in G.
I am not sure about the part where subgroups of cyclic groups are characteristic. If yes, How would you prove this?
I was thinking about using the fact that subgroups of cyclic groups are cyclic, and that subgroups of cyclic groups are (fully)Characteristic (is that true?). Then we would have
K char in H and H normal in G.
Hence K normal in G.
I am not sure about the part where subgroups of cyclic groups are characteristic. If yes, How would you prove this?