Results 1 to 3 of 3

Math Help - A question in group theory.

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    50

    A question in group theory.

    I am given a finite group G with order n. The following mapping is considered G to G: f(x)=x^2. I have to prove that this mapping is bijective only if only n is odd.


    I easily proved that mapping is not bijective when n is even using Cauchy's theorem. How should I prove that it bijective when n is odd?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by andreas View Post
    I am given a finite group G with order n. The following mapping is considered G to G: f(x)=x^2. I have to prove that this mapping is bijective only if only n is odd.


    I easily proved that mapping is not bijective when n is even using Cauchy's theorem. How should I prove that it bijective when n is odd?
    so suppose n=2k + 1. since G is finite, bijectivity of f is equivalent to injectivity. so suppose x^2=y^2. then: x=x^{n+1}=x^{2k+2}=y^{2k+2}=y^{n+1}=y. \ \ \Box
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2008
    Posts
    50
    Quote Originally Posted by NonCommAlg View Post
    so suppose n=2k + 1. since G is finite, bijectivity of f is equivalent to injectivity. so suppose x^2=y^2. then: x=x^{n+1}=x^{2k+2}=y^{2k+2}=y^{n+1}=y. \ \ \Box
    Thank you a lot!!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. another group theory question
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: November 15th 2010, 04:49 AM
  2. Question on group theory
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 27th 2010, 10:14 AM
  3. group theory question
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: June 8th 2009, 02:09 AM
  4. Question in group theory.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 4th 2008, 12:05 AM
  5. Group Theory Question, Dihedral Group
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 4th 2008, 11:36 AM

Search Tags


/mathhelpforum @mathhelpforum