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In earlier work it was shown that each nonabelian finite simple group G has a conjugacy class C such that, whenever 1≠x∈G, the probability is greater than 1/10 that G=〈x,y〉 for a random y∈C. Much stronger asymptotic results were also proved. Here we show that, allowing equality, the bound 1/10 can be replaced by 13/42; and, excluding an explicitly listed set of simple groups, the bound 2/3 holds.We...
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