Results 1 to 3 of 3

Math Help - Finding a generator of a cyclic group

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    79

    Finding a generator of a cyclic group

    I need to show that G15 is a cyclic group by finding a generator.
    I know that the elements of G15 are {1,2,4,7,8,11,13,14}.

    My question is, are every single one of these numbers considered a generator of G15? Or is there more to it??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by steph3824 View Post
    I need to show that G15 is a cyclic group by finding a generator.


    This might prove to be a little hard to achieve since this groups isn't cyclic, but do not believe me: just

    multiply over and over by itself each element modulo 15 and find out at once that none has order 8...

    Tonio



    I know that the elements of G15 are {1,2,4,7,8,11,13,14}.

    My question is, are every single one of these numbers considered a generator of G15? Or is there more to it??
    .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,312
    Thanks
    692
    well there are some shortcuts, for each a ≠ 1 in G15, one need only check a^2 and a^4.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Definition of a generator of a cyclic group?
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: October 10th 2011, 07:18 PM
  2. Finding an inifnite group that is not cyclic
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 3rd 2011, 07:05 PM
  3. Cyclic Group having only one generator
    Posted in the Advanced Algebra Forum
    Replies: 14
    Last Post: August 11th 2011, 07:33 AM
  4. Finding a Generator of a Cyclic Group
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: March 9th 2011, 06:40 PM
  5. [SOLVED] Cyclic groups of order greater then 2 have more then one generator
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 12th 2010, 07:12 PM

Search Tags


/mathhelpforum @mathhelpforum