Results 1 to 4 of 4

Math Help - Help about rep group!

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    3

    Help about rep group!

    Let G be an nonabelian has oder of 8. Let x be a character. Show that x(1)=1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by thanhuthe View Post
    Let G be an nonabelian has oder of 8. Let x be a character. Show that x(1)=1

    A character is always a group homomorphism, so...

    Tonio

    Ps. By the way, the above is true for ANY group, not only non-abelian ones of order 8.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2010
    Posts
    95
    Do you mean a multiplicative character (linear character) or a character of a representation? If you are referring the latter, it is not always true that x(1)=1.

    For example, _8 \rightarrow GL_2(\mathbb{Re})" alt="\phi_8 \rightarrow GL_2(\mathbb{Re})" /> can be a matrix representation (verify this), which maps the identity of D_8 to 2 \times 2 identity matrix in GL_2(\mathbb{Re}), i.e., \chi(1)=2, where \chi is the character of \phi.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jan 2011
    Posts
    3
    Thanks so much!
    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, 01:06 PM
  2. Klein four-group is normal group of A4
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: December 29th 2009, 02:15 PM
  3. Replies: 1
    Last Post: November 4th 2009, 09:52 AM
  4. Quick questions on Group Theory - Cosets / Normal Group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 16th 2009, 08:39 AM
  5. Group Theory Question, Dihedral Group
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 4th 2008, 10:36 AM

Search Tags


/mathhelpforum @mathhelpforum