论文标题
将Kövári-Sós-Turán定理应用于小组理论中的问题
Applying the Kövári-Sós-Turán theorem to a question in group theory
论文作者
论文摘要
令$ m \ leq n $为正整数，而$ \ mathfrak x $一类，该类别针对亚组，商组和扩展名而关闭。假设有限的组$ g $满足每两个子集$ m $和$ n $ carcinalities $ m $和$ n的条件，分别存在$ x \ in m $ in m $和$ y \ in n $，以至于$ \ langle x，y \ rangle x，y \ rangle \ in \ nathfrak in \ mathfrak x. $ $ g \ $ g fe \ left（\ frac {180} {53} \ right）^m（n-1）。$
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 $|G|\leq \left(\frac{180}{53}\right)^m(n-1).$
