Results 1 to 3 of 3

Math Help - Beginning Abstract Algebra Problem

  1. #1
    Super Member
    Joined
    Feb 2008
    Posts
    535

    Beginning Abstract Algebra Problem

    Prove this is true for every group G, or give a counter example to show this is false in some groups:

    If x^2 = a^2, then x=a
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Failure's Avatar
    Joined
    Jul 2009
    From
    Zürich
    Posts
    555
    Quote Originally Posted by jzellt View Post
    Prove this is true for every group G, or give a counter example to show this is false in some groups:

    If x^2 = a^2, then x=a
    Obviously, you need a counterexample to x^2=a^2\Rightarrow x=a. - What about \mathbb{R}\backslash\{0\} with multiplication?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    Another, simpler, example is the set {1, -1} with multiplication as operation. Yet, another, the Klein 4-group. In fact, any finite group whose order is even!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. abstract algebra problem
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 17th 2010, 04:30 PM
  2. Abstract Algebra: a problem about ideals
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 8th 2010, 10:58 PM
  3. abstract algebra hw problem
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: March 16th 2009, 10:07 PM
  4. Abstract algebra homework problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 30th 2008, 08:52 AM
  5. [SOLVED] Abstract Algebra Problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 23rd 2008, 10:56 AM

Search Tags


/mathhelpforum @mathhelpforum