论文标题
关于Sylow子组的简单组生成
On the generation of simple groups by Sylow subgroups
论文作者
论文摘要
让$ g $为有限的简单谎言类型，让$ p $为$ 2 $ -g $ $ g $的sylow $ 2 $。在本文中，我们证明，对于g $中的任何非平凡元素$ x \，存在$ g \ in g $，因此$ g = \ langle p，x^g \ rangle $。通过将这一结果与Breuer和Guralnick的最新工作相结合，我们推断出，如果$ G $是有限的Nonabelian简单组，而$ r $是$ | G | $的任何主要除数，则$ G $由Sylow $ 2 $ -Subgroup和Sylow $ r $ -Subgroup产生。
Let $G$ be a finite simple group of Lie type and let $P$ be a Sylow $2$-subgroup of $G$. In this paper, we prove that for any nontrivial element $x \in G$, there exists $g \in G$ such that $G = \langle P, x^g \rangle$. By combining this result with recent work of Breuer and Guralnick, we deduce that if $G$ is a finite nonabelian simple group and $r$ is any prime divisor of $|G|$, then $G$ is generated by a Sylow $2$-subgroup and a Sylow $r$-subgroup.
