Results 1 to 8 of 8

Math Help - make bx = xb

  1. #1
    Member
    Joined
    Feb 2010
    Posts
    84

    make bx = xb

    how can you make bx = xb without commutative law?

    (you make apply b^(-1) since b = b^(-1)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by rainyice View Post
    how can you make bx = xb without commutative law?

    (you make apply b^(-1) since b = b^(-1)
    This question is not well-formed at all. If x,b are arbitrary this is the commutative law.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2010
    Posts
    84
    Quote Originally Posted by Drexel28 View Post
    This question is not well-formed at all. If x,b are arbitrary this is the commutative law.
    exactly ..... that's why i could not solve it ...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by rainyice View Post
    exactly ..... that's why i could not solve it ...
    Is this supposed to be a group? Then, x=b^{-1}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Feb 2010
    Posts
    84
    I am learning about Group Theory now and is in subgroup session. However, the problem does not say x = b^(-1)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,537
    Thanks
    1392
    Quote Originally Posted by rainyice View Post
    how can you make bx = xb without commutative law?

    (you make apply b^(-1) since b = b^(-1)
    If your group it not commutative and you are not given additional information about b and x, you can't "make" bx and xb equal. In general they aren't.

    Now, what, exactly, was the full statement of the problem?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Feb 2010
    Posts
    84
    Quote Originally Posted by HallsofIvy View Post
    If your group it not commutative and you are not given additional information about b and x, you can't "make" bx and xb equal. In general they aren't.

    Now, what, exactly, was the full statement of the problem?
    the center Z(G) is defined as Z(G) = {a E G | ax = xa for every x E G}
    Prove that if b is the only element of order 2 in G, then b E Z(G)
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Feb 2007
    Posts
    70
    Quote Originally Posted by rainyice View Post
    the center Z(G) is defined as Z(G) = {a E G | ax = xa for every x E G}
    Prove that if b is the only element of order 2 in G, then b E Z(G)
    This is a WAY different question than what you originally asked. It's asking you to prove that if b is the only element of order 2, then it commutes with every element of G.

    Let x \in G and consider xbx^{-1}. What is the order of this element? What does that tell you about its relation to the element b?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Make 42
    Posted in the Math Puzzles Forum
    Replies: 4
    Last Post: April 24th 2010, 10:01 AM
  2. Make a table...
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: March 23rd 2010, 09:28 PM
  3. how to make a derivative by x..
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 17th 2009, 02:20 AM
  4. make 'em =
    Posted in the Math Puzzles Forum
    Replies: 4
    Last Post: July 22nd 2009, 08:52 PM
  5. use only four 4's to make 10
    Posted in the Math Topics Forum
    Replies: 29
    Last Post: September 5th 2008, 10:08 AM

Search Tags


/mathhelpforum @mathhelpforum