论文标题
关于有限组的$ p $元素的数量
On the number of $p$-elements in a finite group
论文作者
论文摘要
在本文中，我们研究了$ p $ emlements的数量和有限群体$ g $的Sylow $ p $ - subgroup的订单。众所周知，该比率是一个积极的整数，我们猜想，对于每个组$ g $，至少是$（1- \ frac {1} {p} {p}）$ - $ g $的Sylow $ P $ -subgroups数量的TH。如果$ g $是$ p $ -solvable，我们证明了这个猜想。此外，如果每个几乎简单的组都有某种相似的条件，我们证明了猜想在其一般性中是正确的。
In this paper we study the ratio between the number of $p$-elements and the order of a Sylow $p$-subgroup of a finite group $G$. As well known, this ratio is a positive integer and we conjecture that, for every group $G$, it is at least the $(1-\frac{1}{p})$-th power of the number of Sylow $p$-subgroups of $G$. We prove this conjecture if $G$ is $p$-solvable. Moreover, we prove that the conjecture is true in its generality if a somewhat similar condition holds for every almost simple group.
