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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- Oct 13th 2011, 12:10 PMtangibleLimeQuick subgroup question
Are all sets generated by each <n> from subgroups? (I know that they are not all generators, and some subgroups contain others)

- Oct 13th 2011, 01:55 PMDevenoRe: Quick subgroup question
what do you mean, "sets generated by <n>"?

- Oct 13th 2011, 01:58 PMtangibleLimeRe: Quick subgroup question
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) - Oct 13th 2011, 03:06 PMDevenoRe: Quick subgroup question
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.