论文信息 - The probability of generating a classical group

The probability of generating a classical group

In [KL] it is provcd that the probability of two randomly chosen elements of a finite dassical simple group G actually generating G tends to 1 as lei increases. If gEe, let Pu(g) be the probability that, if h is chosen randomly in G, then (g, h) IG. Let PG : = ma..x{Pu(g) I 9 E e#}. In [KL, Conjecture 2] it is suggested that a stronger result might hold: Pc ---4 0 as IGI ---4 00 for simple classical groups G. In this paper we investigate this question. It turns out that there is an interesting dichotomy here: while the answer is positiw~ whcn the defining dimension is fixed and the field size increases, this is not so

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