Results 1 to 5 of 5

Math Help - Verification?

  1. #1
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823

    Verification?

    I'm trying to verify my solution to this problem:

    Suppose a and x are both elements in group G. Solve the following equations simultaneously for x:

    x^2=a^2 and x^5=e where e is the identity element of G

    OK. I find that x=(a^4)^{-1}.

    I'm having trouble verifying this result. CAN I verify?

    *note: x*x=x^2 is an example of the notation employed here.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,391
    Thanks
    758

    Re: Verification?

    what do you mean by verify?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2

    Re: Verification?

    Well, you can do this:

    (a^{-4})^{5}=a^{-20}=(a^{2})^{-10}\dots, and see if you get e.

    I would also work by attempting to compute the order of a. That might help you verify what

    (a^{-4})^{2} is.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2011
    Posts
    58

    Re: Verification?

    x^2 (a^2)^{-1} = e = x^5

    (a^2)^{-1} = x^{-1}x^{-1} x^5 = x^3 = x^2 x = a^2 x

    a^{-1}a^{-1}(a^2)^{-1}=x

    Note that xa^4=(a^{-1}a^{-1}(a^2)^{-1})(a^4)=a^{-1}a^{-1}(a^2)^{-1}a^2aa=e

    So since inverses are unique x=(a^4)^{-1}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,391
    Thanks
    758

    Re: Verification?

    the reason for my question, in my earlier post, is that simultaneous equations like this aren't like what you may be used to, where you "plug in the value for x" and see if it works.

    we aren't told what a is (or even what the group operation is), so there's not some kind of computational verification you can do.

    if you have derived a value of x in terms of a correctly (using the group axioms properly), that's all the verification you need (as in the post above, and i think there was an earlier thread on this same topic).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. simple verification
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 19th 2010, 07:15 PM
  2. Quick verification of something...
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: December 15th 2009, 05:58 PM
  3. Inequality Verification
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 20th 2009, 07:51 AM
  4. verification needed
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 15th 2009, 01:32 AM
  5. Verification!
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: April 21st 2009, 02:23 PM

Search Tags


/mathhelpforum @mathhelpforum