Results 1 to 2 of 2

Math Help - group theory question

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    50

    group theory question

    prove that if G is a finite group that the number of elements in G is even
    So
    e≠x belong to G (e is the neutral element)
    that provide x^2 = e (in other words: x=x^-1).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
    Posts
    802
    Hello,

    Let A=\left\{x\ :\ x\in G\ \text{and}\ x\neq x^{-1}\right\} and B=\left\{x\ :\ x\in G\ \text{and}\ x=x^{-1}\right\}. We have A\cap B=\emptyset and G=A\cup B so |G|=|A|+|B|. Can you show that |B| is even and that there exists an element x\neq e lying in B?
    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, 03:49 AM
  2. Question on group theory
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 27th 2010, 09:14 AM
  3. group theory question
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: June 8th 2009, 01:09 AM
  4. A question in group theory.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 10th 2008, 11:38 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