Results 1 to 3 of 3

Math Help - Prove a Group is NOT cyclic

  1. #1
    Member Ranger SVO's Avatar
    Joined
    Apr 2006
    From
    Abilene Tx
    Posts
    90

    Prove a Group is NOT cyclic

    How would I show that a group of positve rational numbers under multiplication is not cyclic.

    I can see that its true, but how would I prove it
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Ranger SVO View Post
    How would I show that a group of positve rational numbers under multiplication is not cyclic.

    I can see that its true, but how would I prove it
    Perhaps proof by contradiction. Assume there's an element g that generates all the other elements.
    Last edited by mr fantastic; February 2nd 2008 at 01:51 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Ranger SVO View Post
    How would I show that a group of positve rational numbers under multiplication is not cyclic.

    I can see that its true, but how would I prove it
    Suppose it is. Let x be the generator. If x is an integer then x^n is an integer which means it cannot generate the non-integers. If x is a non-integer then x^n is a non-integer which means it cannot generate the integers.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove quotient group cyclic
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 10th 2011, 05:54 AM
  2. Prove for cyclic group
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: June 6th 2011, 10:47 AM
  3. Prove that group of order 15 is cyclic
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: April 10th 2011, 01:14 AM
  4. Prove that a quotient group is cyclic
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 8th 2010, 02:13 AM
  5. Prove cyclic subroups => cyclic group
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: October 11th 2009, 07:36 PM

Search Tags


/mathhelpforum @mathhelpforum