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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


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    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).
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