Results 1 to 3 of 3

Math Help - Deducing a relation from others

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    36

    Deducing a relation from others

    Hello, I'm trying to deduce the relation xy^4 = y^4 x from xy^2 = y^3 x and yx^3 = x^2y. So far I've gotten:

    [x,y^4] = x^{-1} y^{-4} xy^4 = x^{-1}y^{-4}(xy^2)y^2 = x^{-1} y^{-1} (xy^2) = x^{-1}y^{-1} y^3 x = x^{-1}y^2x

    However, everything I try from this point onwards seems to make it more complicated. Any help would be greatly appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member nimon's Avatar
    Joined
    Sep 2009
    From
    Edinburgh, UK
    Posts
    64
    Hmm...

    Suppose that xy^{4}=y^{4}x is true and that xy^{2} = y^{3}x and yx^{3} = x^{2}y. Then

    xy^{4} = y^{6}x = y^{4}x \Rightarrow y^{2}= e \Rightarrow x = yx \Rightarrow y \,\,\text{is the identity}

    But then x^{3} = x^{2} \Rightarrow x \,\,\text{is the identity.} This would be a consequence of these relations; does this make sense in the group your considering? I only ask because its nice to know that it's plausible to derive the first relation from the other two before you begin. If x,y are definitely not the identity element then you needn't waste your time!

    Please make sure I haven't made a silly mistake because I excel at those.
    Last edited by nimon; April 9th 2010 at 04:41 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2010
    Posts
    36
    Well the question asks for this group with presentation \langle x, y \mid xy^2 = y^3 x, yx^3 = x^2 y \rangle. No other relations are given and the 3rd relation was given as a hint. I arrived at the same conclusion as you, but I just can't seem to get the third relation.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: May 2nd 2011, 04:16 AM
  2. Help in deducing!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 17th 2010, 02:07 AM
  3. Deducing polynomials technique
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 4th 2010, 03:46 AM
  4. Deducing matrix from minimum polynomial
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 12th 2009, 01:40 AM
  5. deducing a limit...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 2nd 2008, 06:15 AM

Search Tags


/mathhelpforum @mathhelpforum