论文标题
根据素数界定有限组的类数量
Bounding the number of classes of a finite group in terms of a prime
论文作者
论文摘要
Héthelyi和Külshammer表明，任何可解决的有限群体$ g $的共轭类别$ k（g）$的数量，其订单可以由Prime $ p $的平方排除，至少为$（49p+1）/60 $。在这里，建立了该结果的渐近概括。事实证明，存在一个常数$ c> 0 $，因此对于任何有限的$ g $，其订单可以由prime $ p $的平方排除，我们有$ k（g）\ geq cp $。
Héthelyi and Külshammer showed that the number of conjugacy classes $k(G)$ of any solvable finite group $G$ whose order is divisible by the square of a prime $p$ is at least $(49p+1)/60$. Here an asymptotic generalization of this result is established. It is proved that there exists a constant $c>0$ such that for any finite group $G$ whose order is divisible by the square of a prime $p$ we have $k(G) \geq cp$.
