Results 1 to 4 of 4

Math Help - cyclic group

  1. #1
    Newbie
    Joined
    Jun 2012
    From
    kolkata
    Posts
    7

    cyclic group

    i need a clue to prove this. can any one please help?
    If a & b be elements of a group G, & o(a)=m (read order of a= m) and o(b)= n and gcd(m,n)=1
    then <a> (intersection) <b>= {identity}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: cyclic group

    Quote Originally Posted by srv123 View Post
    i need a clue to prove this. can any one please help?
    If a & b be elements of a group G, & o(a)=m (read order of a= m) and o(b)= n and gcd(m,n)=1
    then <a> (intersection) <b>= {identity}
    Welcome to MHF, srv123!

    Suppose the intersection is not empty.
    That means there must be an element c=a^i=b^j with i<m and j<n.
    Can you draw any conclusions about this element (leading to a contradiction)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2012
    From
    kolkata
    Posts
    7

    Re: cyclic group

    thanks...
    i get it...o(c) must divide both m and n but they are co-prime...
    thanks again..
    had a good experience on the 1st day
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: cyclic group

    You're welcome!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Order of Group. Direct Product of Cyclic Group
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: November 19th 2011, 02:06 PM
  2. cyclic group
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 3rd 2010, 07:35 PM
  3. cyclic group help
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 4th 2010, 04:25 PM
  4. Prove cyclic subroups => cyclic group
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: October 11th 2009, 08:36 PM
  5. automorphism group of a cyclic group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 10th 2009, 07:38 PM

Search Tags


/mathhelpforum @mathhelpforum