Abstract
Let σ, π be two permutations selected at random from the uniform distribution on the symmetric group Sn. By a result of Dixon [5], the subgroup G generated by σ, π is almost always (i.e. with probability approaching 1 as n → ∞) either Sn or the alternating group An. We prove that the diameter of the Cayley graph of G defined by {σ, π} is almost always not greater than exp ((½ + o(l)). (In n)2).
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