Are all sets generated by each <n> from subgroups? (I know that they are not all generators, and some subgroups contain others)
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what do you mean, "sets generated by <n>"?
For example, if ,
<1>, <2>, <3>, <4>
(which are all , so maybe that's a bad example, but I think it gets my intention across)
are you asking if <k> = for every k in , or are you asking if every subgroup of is cyclic (and thus equal to <k> for some k)?
the answer to the first is no, the answer to the second is yes.
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