论文标题
有限简单组的Liebeck和Shalev直径界限的概括
A generalization of the diameter bound of Liebeck and Shalev for finite simple groups
论文作者
论文摘要
令$ g $为非亚伯有限的简单组。 Liebeck和Shalev的著名结果是，每当$ g $中的非平凡的普通子集中，有一个绝对常数的$ c $，然后是$ g $，然后是$ s^{k} = g $，对于任何整数$ k $，至少$ c \ cdot（\ log | g | g |/\ log | s | s |）$。通过证明存在一个绝对常数$ c $，以便每当$ s_ {1}，\ ldots，s_ {k} $是$ g $中的正常子集，with $ \ prod_ {i = 1}^{k} {k} | s_ {i} | s_ {i} | \ geq {| g |}^{c} $，然后$ s_ {1} \ cdots s_ {k} = g $。
Let $G$ be a non-abelian finite simple group. A famous result of Liebeck and Shalev is that there is an absolute constant $c$ such that whenever $S$ is a non-trivial normal subset in $G$ then $S^{k} = G$ for any integer $k$ at least $c \cdot (\log|G|/\log|S|)$. This result is generalized by showing that there exists an absolute constant $c$ such that whenever $S_{1}, \ldots , S_{k}$ are normal subsets in $G$ with $\prod_{i=1}^{k} |S_{i}| \geq {|G|}^{c}$ then $S_{1} \cdots S_{k} = G$.
