拟本原与半本原群的可区别数
The distinguishing number of quasiprimitive and semiprimitive groups
摘要：
$G \leqslant \sym(Ω)$的区别数是$Ω$的分区的最小大小，使得仅$G$的标识固定分区的所有部分。推广了Cameron，Neumann，Saxl和Seress关于有限本原群的可区别数的结果，证明了所有非本原拟本原群都有可区别数2，所有非拟本原半本原群都有可区别数2，除了作用在$\mathbb F_2^3$的8个非零向量上的$\mathrm{GL}(2, 3)$有可区别数3.
英文摘要：
The distinguishing number of $G \leqslant \sym(Ω)$ is the smallest size of a partition of $Ω$ such that only the identity of $G$ fixes all the parts of the partition. Extending earlier results of Cameron, Neumann, Saxl and Seress on the distinguishing number of finite primitive groups, we show that all imprimitive quasiprimitive groups have distinguishing number two, and all non-quasiprimitive semiprimitive groups have distinguishing number two, except for $\mathrm{GL}(2, 3)$ acting on the eight non-zero vectors of $\mathbb F_2^3$, which has distinguishing number three.
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。
