Thread: Quick subgroup question

Are all sets generated by each <n> from subgroups? (I know that they are not all generators, and some subgroups contain others)

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.