Baer-Suzuki定理的进一步可解类似物和不可解群的生成
Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groups
摘要：
设$G$是几乎单群.证明了如果$x \in G$具有素数阶$p \ge 5$，则存在对合$y$使得$<x,y>$不可解.此外，如果$x$是对合，则存在生成不可解群的$x$的三个共轭，除非$x$属于明确描述的例外的简短列表。我们还证明了如果$x$有阶$6$或$9$，则存在两个共轭生成一个不可解群.
英文摘要：
Let $G$ be an almost simple group. We prove that if $x \in G$ has prime order $p \ge 5$, then there exists an involution $y$ such that $<x,y>$ is not solvable. Also, if $x$ is an involution then there exist three conjugates of $x$ that generate a nonsolvable group, unless $x$ belongs to a short list of exceptions, which are described explicitly. We also prove that if $x$ has order $6$ or $9$, then there exists two conjugates that generate a nonsolvable group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
