论文标题
关于生成有限简单组的可能性
On the probability of generating invariably a finite simple group
论文作者
论文摘要
令$ g $为有限的简单组。在本文中，我们考虑存在小本集$ a $ g $的属性，如果$ y \ in g $在g $中随机选择，那么使用高概率$ y $与$ a $的某些元素一起产生$ g $。我们在这个方向上证明了各种结果，无论是正面还是负面。作为推论，我们证明，有限的谎言类型的有限简单组的两个随机选择的元素总是会产生，而概率却远离零。我们的方法基于Fulman和Guralnick的Boston-Shalev猜想的积极解决方案，以及一组谎言类型的属性及其Weyl组的结构之间的某些连接。
Let $G$ be a finite simple group. In this paper we consider the existence of small subsets $A$ of $G$ with the property that, if $y \in G$ is chosen uniformly at random, then with high probability $y$ invariably generates $G$ together with some element of $A$. We prove various results in this direction, both positive and negative. As a corollary, we prove that two randomly chosen elements of a finite simple group of Lie type of bounded rank invariably generate with probability bounded away from zero. Our method is based on the positive solution of the Boston--Shalev conjecture by Fulman and Guralnick, as well as on certain connections between the properties of invariable generation of a group of Lie type and the structure of its Weyl group.
