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Math Help - Cyclic groups?

  1. #1
    Member Jason Bourne's Avatar
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    Cyclic groups?

    (a) Define what it means for s group to be cyclic.

    (b) Give an example of an infinite cyclic group

    (c) Determine whether the group U[15] = {1,2,4,7,8,11,13,14}, where multiplication is mod 15, is cyclic.
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    Quote Originally Posted by Jason Bourne View Post
    (a) Define what it means for s group to be cyclic.
    That is something you need to know from your textbook.

    (b) Give an example of an infinite cyclic group
    \mathbb{Z}
    (c) Determine whether the group U[15] = {1,2,4,7,8,11,13,14}, where multiplication is mod 15, is cyclic.
    Can you find a generator?
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  3. #3
    Member Jason Bourne's Avatar
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    No, I cannot find any generators, so the group is not cyclic.
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    Quote Originally Posted by Jason Bourne View Post
    No, I cannot find any generators, so the group is not cyclic.
    That is correct. In general if n>1 then the group \mathbb{Z}_n^{\text{x}} is cyclic if and only if n=2,4,p^k,2p^k where p is an odd prime.
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