If is a cyclic normal subgroup of I need to prove that any subgroup of is also a normal subgroup of . This seems trivial but I'm not sure that it is.
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Originally Posted by d_p_osters If is a cyclic normal subgroup of I need to prove that any subgroup of is also a normal subgroup of . This seems trivial but I'm not sure that it is. If X has generator a, and Z is a subgroup of X, generated by , then Z is the set of all elements of the form . If , then is generated by , from which you can see that .
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