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Math Help - Quick subgroup question

  1. #1
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    Quick subgroup question

    Are all sets generated by each <n> from \mathbb{Z}_n subgroups? (I know that they are not all generators, and some subgroups contain others)
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  2. #2
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    Re: Quick subgroup question

    what do you mean, "sets generated by <n>"?
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  3. #3
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    Re: Quick subgroup question

    For example, if \mathbb{Z}_{5},

    <1>, <2>, <3>, <4>

    (which are all \mathbb{Z}_{5}, so maybe that's a bad example, but I think it gets my intention across)
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  4. #4
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    Re: Quick subgroup question

    are you asking if <k> = \mathbb{Z}_n for every k in \mathbb{Z}_n, or are you asking if every subgroup of \mathbb{Z}_n 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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