Without using the classification of finite simple groups (CFSG), we show that the probability that two random elements of generate a primitive group smaller than is at most . As a corollary we get Dixon's asymptotic expansion

中文翻译：

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没有有限单群分类的 Dixon 渐近

在不使用有限简单群分类（CFSG）的情况下，我们证明了两个随机元素的概率生成一个小于的原始群至多是。作为推论，我们得到 Dixon 的渐近展开式