发表机构
School of Mathematical Sciences, Peking University（北京大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究解决了《Kourovka笔记》中问题17.112(a)，明确了存在真非平凡普通$G$-可置换子群的非阿贝尔有限单群类型，并对其相关子群完成分类，其余此类群无该类子群。
AI 中文摘要
我们完全解决了《Kourovka笔记》中问题17.112的(a)部分。证明了非阿贝尔有限单群$G$存在真非平凡普通$G$-可置换子群当且仅当$G$同构于满足$q\geq4$且$q\not\equiv3\pmod4$的素幂${\rm PSL_2(q)}$、$a\geq1$的${}^2B_2(2^{2a+1})$、$J_1$、${\rm Sp}_4(4)$，或满足$p$为素数且$p\equiv1,13,17\pmod{24}$的${\rm PSp}_4(p)$；此外，我们对这些群的所有真非平凡普通$G$-可置换子群进行了分类，其余非阿贝尔有限单群$G$均无此类子群。
英文摘要
We completely solve part (a) of Problem 17.112 in the Kourovka Notebook. We prove that a non-abelian finite simple group $G$ has a proper non-trivial ordinary $G$-permutable subgroup if and only if $G$ is isomorphic to ${\rm PSL_2(q)}$ where $q\geq4$ is a prime power and $q\not\equiv3\pmod4$, ${}^2B_2(2^{2a+1})$ where $a\geq1$, $J_1$, ${\rm Sp}_4(4)$, or ${\rm PSp}_4(p)$ where $p$ is prime and $p\equiv1,13,17\pmod{24}$. Moreover, we classify all proper non-trivial ordinary $G$-permutable subgroups of these groups. Every other non-abelian finite simple group $G$ has no proper non-trivial ordinary $G$-permutable subgroup.
CommentsThis completely solves Problem 17.112(a) of the Kourovka Notebook
