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Math Help - subgroup

  1. #1
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    subgroup

    Q: list all subgroup of a cyclic group of order 30.

    give the hint to do this.
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  2. #2
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    The subgroups of any finite cyclic group can be determined the same way:

    There is exactly one cyclic subgroup of every order which divides the order of the group.

    Of course, this makes answering the question easy: the subgroups of \mathbb{Z}_{30} are \mathbb{Z}_{30},\mathbb{Z}_{15},\mathbb{Z}_{10},\m  athbb{Z}_6,\mathbb{Z}_5,\mathbb{Z}_3,\mathbb{Z}_2,  \mathbb{Z}_1=\{ e\}.

    But see if you can prove the statement above on WHY the subgroups of a cyclic group look this way.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by topspin1617 View Post
    Of course, this makes answering the question easy: the subgroups of \mathbb{Z}_{30} are \mathbb{Z}_{30},\mathbb{Z}_{15},\mathbb{Z}_{10},\m  athbb{Z}_6,\mathbb{Z}_5,\mathbb{Z}_3,\mathbb{Z}_2,  \mathbb{Z}_1=\{ e\}.
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