Results 1 to 2 of 2

Math Help - If x^(2)=1 then G is abelian

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    38

    If x^(2)=1 then G is abelian

    I'm trying to show that if x^(2)=1 for all x in G then G is an abelian group.


    Attempt at the solution:

    xx=1

    x=x^(-1)

    xy=(xy)^(-1)

    xy=y^(-1)x^(-1)=yx

    Does this look correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    Posts
    677
    Quote Originally Posted by Louise View Post
    I'm trying to show that if x^(2)=1 for all x in G then G is an abelian group.


    Attempt at the solution:

    xx=1

    x=x^(-1)

    xy=(xy)^(-1)

    xy=y^(-1)x^(-1)=yx

    Does this look correct?
    yes - looks neat to me
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: June 6th 2010, 03:09 AM
  2. is it abelian
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 22nd 2010, 06:11 AM
  3. Is G abelian?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 12th 2009, 03:57 AM
  4. 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
  5. Problem: Abelian/non-abelian subgroups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 4th 2009, 01:10 PM

Search Tags


/mathhelpforum @mathhelpforum