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Abstract Let G be a finite simple group. A conjecture of J. D. Dixon, which is now a theorem (see [2, 5, 9]), states that the probability that two randomly chosen elements x, y of G generate G tends to 1 as ∣G∣→∞. Geoff Robinson asked whether the conclusion still holds if we require further that x, y are conjugate in G. In this note we study the probability Pc(G) that 〈x, xy〉 = G, where x, y∈G are chosen at random (with uniform distribution on G×G). We shall show that Pc(G)→1 as ∣G∣→∞ if G is an alternating group, or a projective special linear group, or a classical group of bounded dimension. In fact, some (but not all) of the exceptional groups of Lie type will also be dealt with. 1991 Mathematics Subject Classification 20E18, 20E07. © London Mathematical Society
Bulletin of the London Mathematical Society – Oxford University Press
Published: Sep 1, 1997
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