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.

中文翻译：

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关于有限群中p元素的个数

在本文中，我们研究了有限群G的p元素数与Sylow p子群的阶数之比。众所周知，该比率是一个正整数，我们推测，对于每个组G，它至少是Sylow p数的\（（1- \ frac {1} {p}）\） -次幂-subgroups的ģ。如果G是p可解的，我们证明了这个猜想。此外，我们证明，如果对于每个几乎简单的组都存在某种相似的条件，则该猜想在总体上是正确的。