The Probability of Generating the Symmetric Group

@inproceedings{BOVEY1978ThePO,
  title={The Probability of Generating the Symmetric Group},
  author={JOHN BOVEY and ALAN WILLIAMSON},
  year={1978}
}
  • JOHN BOVEY, ALAN WILLIAMSON
  • Published 1978
In [2], Dixon considered the following question: " Suppose two permutations are chosen at random from the symmetric group Sn of degree n. What is the probability that they will generate Sn? " Actually, Netto conjectured last century that almost all pairs of elements from Sn will generate Sn or An. Dixon showed that this is true in the following sense: The proportion of ordered pairs (x, y) (x, y e Sn) which generate either An or Sn is greater than 1 — 2/(log log n) 2 for all sufficiently large… CONTINUE READING
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