从Thompson到Baer-Suzuki：可解radical的一个尖锐刻画
From Thompson to Baer-Suzuki: a sharp characterization of the solvable radical
摘要：
我们证明了素数阶元$g$属于有限群（或更一般地说，线性群）的可解根$R(G)$当且仅当对每个$x\in G$，由$g, xgx^{-1}$生成的子群是可解的.这个定理意味着有限（或线性）群$G$是可解的当且仅当在$G$的每个共轭类中每两个元素生成一个可解子群。
英文摘要：
We prove that an element $g$ of prime order $>3$ belongs to the solvable radical $R(G)$ of a finite (or, more generally, a linear) group if and only if for every $x\in G$ the subgroup generated by $g, xgx^{-1}$ is solvable. This theorem implies that a finite (or a linear) group $G$ is solvable if and only if in each conjugacy class of $G$ every two elements generate a solvable subgroup.
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。
