Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to prove that if x^n*y=y*x^n, then x and y commute

  1. Apr 16, 2010 #1
    Let x and y be elements of a group.

    I can see that it works the other way, i.e. if x and y commute, then y*x^n = x^n*y...
     
  2. jcsd
  3. Apr 16, 2010 #2

    Gib Z

    User Avatar
    Homework Helper

    Write down the equation that represents x and y commuting, and then the equation you have beneath it. How can you make the second one become the first?
     
  4. Apr 16, 2010 #3
    Is it necessarily true?
    What about the case where x and y don't commute, but xn=E for some specific n?
     
  5. Apr 16, 2010 #4

    Gib Z

    User Avatar
    Homework Helper

    Sorry, I'm used to seeing n representing a general positive integer so I assumed that was the case here as well.
     
  6. Apr 16, 2010 #5
    Well, the problem with that is n either has a specific value or is a general integer...if it's a general integer, then it's trivial to consider the case n=1. So I'm assuming that's not what is meant.
     
  7. Apr 16, 2010 #6
    Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to prove that if x^n*y=y*x^n, then x and y commute
  1. X^y=y^x proof (Replies: 4)

Loading...