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

Group Theory Problem

  1. Sep 24, 2009 #1
    This is from Wikipedia's "unsolved problems in math" section:

    Finding a formula for the probability that two elements chosen at random generate the symmetric group Sn

    Can someone explain that to me? I know what Sn is. What are these two "elements"?
  2. jcsd
  3. Sep 24, 2009 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I'm not sure what's unclear. As the article said, the "elements" are random variables -- presumably independent and uniformly distributed.

    If X and Y are random variables with domain Sn, then <X,Y> is a random variable whose domain is the set of all subgroups of Sn. The question is to find a formula for P(<X,Y>=Sn).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Group Theory Problem