Kövári-Sós-Turán定理在群论中的应用
Applying the Kövári-Sós-Turán theorem to a question in group theory
摘要：
设$m\leq n$是正整数，$\mathfrak X$是子群、商群和扩张闭的群类.设有限群$G$满足条件：对于基数分别为$m$和$n,$的每两个子集$M$和$N$，存在$x \in M$和$y \in N$，使得$\langle x, y \rangle\in \mathfrak X.$，则$G\in \mathfrak X$或$|G|\leq \left(\frac{180}{53}\right)^m(n-1).$
英文摘要：
Let $m\leq n$ be positive integers and $\mathfrak X$ a class of groups which is closed for subgroups, quotient groups and extensions. Suppose that a finite group $G$ satisfies the condition that for every two subsets $M$ and $N$ of cardinalities $m$ and $n,$ respectively, there exist $x \in M$ and $y \in N$ such that $\langle x, y \rangle\in \mathfrak X.$ Then either $G\in \mathfrak X$ or $|G|\leq \left(\frac{180}{53}\right)^m(n-1).$
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。
