Results 1 to 3 of 3

Math Help - Proving a group to be abelian

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    21

    Proving a group to be abelian

    Prove that if x = x^-1 for all x in the group G, then G is abelian.

    I'm getting nowhere with this after several attempts. Can someone offer insight?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Dinkydoe's Avatar
    Joined
    Dec 2009
    Posts
    411
    Let a,b\in G. We need to show that ab=ba.
    Since ab = (ab)^{-1} we have ab=(ab)^{-1}= b^{-1}a^{-1}= ba
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Alternatively, a=a^{-1}\implies a^2=e. So ab=a\left(ab\right)^2b=\left(a^2\right)ba\left(b^2  \right)=ba
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving an abelian group properties
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 24th 2011, 03:06 AM
  2. Is the subgroup of an abelian group always abelian?
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: December 6th 2009, 11:38 PM
  3. Abelian Group 2.12
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 1st 2009, 12:01 AM
  4. Abelian Group
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 16th 2009, 07:14 PM
  5. Proving a group is Abelian...
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: September 27th 2007, 12:20 AM

Search Tags


/mathhelpforum @mathhelpforum