Results 1 to 6 of 6

Math Help - homomorphism and subgroup question

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    51

    homomorphism and subgroup question

    Let k|n. Consider :U(n) to U(n) defined by (x)=x mod k. What is the relationship between this homomorphism and the subgroup Uk(n) of U(n).
    No idea on this one. Help would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by wutang View Post
    Let k|n. Consider :U(n) to U(n) defined by (x)=x mod k. What is the relationship between this homomorphism and the subgroup Uk(n) of U(n).
    No idea on this one. Help would be greatly appreciated.
    What are U(n) and Uk(n)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2010
    Posts
    51
    U(n) is defined to be the group with the numbers relative prime up to n (such that the gcd between n and an x in U(n) is 1). For example U(9)=1,2,4,5,7,8. Uk(n) is defined as the set of x's that are an element of U(n) s.t. x mod k=1. For example U7(105)={1,8,22,29,43,64,71,92}.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by wutang View Post
    U(n) is defined to be the group with the numbers relative prime up to n (such that the gcd between n and an x in U(n) is 1). For example U(9)=1,2,4,5,7,8. Uk(n) is defined as the set of x's that are an element of U(n) s.t. x mod k=1. For example U7(105)={1,8,22,29,43,64,71,92}.
    Well, isn't Uk(n)=\ker f?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Apr 2010
    Posts
    51
    Let k|n. Consider :U(n) to U(k) defined by (x)=x mod k. What is the relationship between this homomorphism and the subgroup Uk(n) of U(n).
    Sorry there should have been a k in the second u and not an n. So the kernel is the set of elements x in the domain that map to the identity element in the co domain. Since Uk(n) = x element of U(n) s.t. x mod k = 1, then Uk(n) would just be the kernel of f. Is this what you are saying because this seems right, but really easy for some reason.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by wutang View Post
    Let k|n. Consider :U(n) to U(k) defined by (x)=x mod k. What is the relationship between this homomorphism and the subgroup Uk(n) of U(n).
    Sorry there should have been a k in the second u and not an n. So the kernel is the set of elements x in the domain that map to the identity element in the co domain. Since Uk(n) = x element of U(n) s.t. x mod k = 1, then Uk(n) would just be the kernel of f. Is this what you are saying because this seems right, but really easy for some reason.
    Seems right to me, but probability that I got this wrong is not almost surely zero.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. homomorphism question
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: May 2nd 2010, 02:56 PM
  2. homomorphism question
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 26th 2010, 06:25 PM
  3. Homomorphism question
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 21st 2010, 08:32 PM
  4. normal subgroup, homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 13th 2009, 06:02 PM
  5. mapping homomorphism and subgroup
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 27th 2009, 09:36 AM

Search Tags


/mathhelpforum @mathhelpforum